Ratio, Proportion, Indices, Logarithm

The ratio of two numbers are $\displaystyle 3:4$. The difference of their squares is $\displaystyle 28$ greater is:

The price of scooter and moped are in the ratio $\displaystyle 7:9$. The price of moped is $\displaystyle ₹1,600$ more than that of scooter. Then the price of moped is:

If $\displaystyle A:B=3:7$, then $\displaystyle 3a+2b:4a+5b=?$

The ratio of number of boys and the number of girls in a school is found to be $\displaystyle 15:32$. How many boys and equal number of girls should be added to bring the ratio to $\displaystyle 1:2$?

In a certain business A and B received profit in certain ratio B and C received profits in the same ratio. If A gets $\displaystyle ₹1600$ and C gets $\displaystyle ₹2500$ then how much does B get?

The ratio of two quantities is $\displaystyle 15:17$. If the consequent of its inverse ratio is $\displaystyle 15$, then the antecedent is:

Incomes of R and S are in the ratio $\displaystyle 7:9$ and their expenditures are in the ratio $\displaystyle 4:5$. Their total expenditure is equal to income of R. What is the ratio of their savings?

A bag contains $\displaystyle 105$ coins containing some $\displaystyle 50$ paise, and $\displaystyle 25$ paise coins. The ratio of the number of these coins is $\displaystyle 4:3$. The total value (in $\displaystyle ₹$) in the bag is

In a department, the number of males and females are in the ratio $\displaystyle 3:2$. If $\displaystyle 2$ males and $\displaystyle 5$ females join the department, then the ratio becomes $\displaystyle 2:1$. Initially, the number of females in the department is

A group of $\displaystyle 400$ soldiers at border area had a provision for $\displaystyle 31$ days. After $\displaystyle 28$ days $\displaystyle 280$ soldiers from this group were called back. Find the number of days for which the remaining ration will be sufficient?

The mean proportional between $\displaystyle 24$ and $\displaystyle 54$ is:

If $\displaystyle a:b=9:4$, then $\displaystyle \sqrt{\frac{a}{b}} + \sqrt{\frac{b}{a}}=?$

The mean proportional between $\displaystyle 12x^2$ and $\displaystyle 27y^2$ is:

P, Q and R three cities. The ratio of average temperature between P and Q is $\displaystyle 11:12$ and that between P and R is $\displaystyle 9:8$. The ratio between the average temperature Q and R

For $\displaystyle p, q, r, s > 0$ the value of each ratio is $\displaystyle \frac{p-q}{q+r} = \frac{r-s}{s+p} = \frac{p+q}{q+r}$

Let $\displaystyle x, y$ and $\displaystyle z$ are three positive numbers and $\displaystyle P = \frac{x+y+z}{2}$; $\displaystyle (p-x):(p-y):(p-z) = 3:5:7$ then the ratio of $\displaystyle x:y:z$ is

The ratio compounded of $\displaystyle 2:3, 9:4, 5:6$ and $\displaystyle 8:10$ is

The sub-triplicate ratio of $\displaystyle 8:27$

If $\displaystyle x+y, y+z, z+x$ are in the ratio $\displaystyle 6:7:8$ and $\displaystyle x+y+z = 14$ then the value of $\displaystyle x$ is.

If $\displaystyle x:y:z = 2:3:5$ if $\displaystyle x+y+z = 60$, then the value of $\displaystyle z$

If $\displaystyle \frac{p}{q} = \frac{2}{3}$ then the value of $\displaystyle \frac{2p-q}{2p+q}$

The ratio of two numbers is $\displaystyle 15:19$. If a certain number is added to each term of the ratio it become $\displaystyle 8:9$. What is the number added to each of the ratio?

The salaries of A, B and C are in the ratio $\displaystyle 2:3:5$. If increments of $\displaystyle 15\%$, $\displaystyle 10\%$ and $\displaystyle 20\%$ are allowed respectively to their salary, then what will be the new ratio of their salaries?

If $\displaystyle A:B=5:3$, $\displaystyle B:C=6:7$ and $\displaystyle C:D=14:9$ then the value of $\displaystyle A:B:C:D$ is:

A vessel contained a solution of acid and water in which water was $\displaystyle 64\%$. Four liters of the solution were taken out of the vessel and the same quantity of water was added. If the resulting solution contains $\displaystyle 30\%$ acid, the quantity (in liters) of the solution, in the beginning in the vessel, was

A box contains $\displaystyle 25$ paise coins and $\displaystyle 10$ paise coins and $\displaystyle 5$ paise coins in ratios $\displaystyle 3:2:1$ and total money is $\displaystyle ₹40$. How many $\displaystyle 5$ paise coins are there?

If $\displaystyle x:y=4:6$ and $\displaystyle z:x=4:16$ find $\displaystyle Y$?

A fraction becomes $\displaystyle 1$ when $\displaystyle 3$ is added to the numerator and $\displaystyle 1$ is added to the denominator, but when the numerator and denominator are decreased by $\displaystyle 2$ and $\displaystyle 1$ respectively, it becomes $\displaystyle 1/2$. The denominator of the fraction is:

If the four number $\displaystyle 1/4, 1/6, 1/10, \text{ and } 1/x$ are proportional, then what is the value of $\displaystyle x$?

The ratio of the prices of two houses was $\displaystyle 16:23$. Two years later when the price of the first has increased by $\displaystyle 10\%$ and that of the second by $\displaystyle \text{Rs.} 477$, the ratio of the prices becomes $\displaystyle 11:20$. Find the original prices of the two houses.

On Simplification $\displaystyle \frac{1}{1+z^{a-b}+z^{a-c}} + \frac{1}{1+z^{b-c}+z^{b-a}} + \frac{1}{1+z^{c-a}+z^{c-b}}$ would reduces to

A bag contains $\displaystyle \text{Rs.} 187$ in the form $\displaystyle 1$ rupee, $\displaystyle 50$ paise and $\displaystyle 10$ paise coins in the ratio $\displaystyle 3:4:5$. Find the number of each type of coins.

The ratio of the number of boys and girls in a school is $\displaystyle 2:5$. If there are $\displaystyle 280$ students in the school, find number of girls in the school

If $\displaystyle \frac{p}{q} = \frac{2}{3}$, then the value of $\displaystyle \frac{2p-q}{2p+q}$ is:

The salaries of $\displaystyle A, B$ and $\displaystyle C$ are of ratio $\displaystyle 2:3:5$. If the increments of $\displaystyle 15\%, 10\%$ and $\displaystyle 20\%$ are done their respective salaries, then find new salaries.

The salary of $\displaystyle P$ is $\displaystyle 25\%$ lower than that of $\displaystyle Q$ and the salary of $\displaystyle R$ is $\displaystyle 20\%$ higher than $\displaystyle Q$, the ratio of salary of $\displaystyle R$ and $\displaystyle P$ will be:

If $\displaystyle x:y = 3:5$, then find $\displaystyle \left(1+\frac{1}{x}\right):\left(1+\frac{1}{y}\right)$

If $\displaystyle A:B = 3:4$ and $\displaystyle B:C = 7:9$, $\displaystyle C:D = 2:3$ and $\displaystyle D$ is $\displaystyle 50\%$ more than $\displaystyle E$, find the ratio between $\displaystyle A$ and $\displaystyle E$

The third proportional between $\displaystyle (a^2-b^2)$ and $\displaystyle (a+b)^2$ is:

If $\displaystyle \frac{p}{q} = \frac{r}{s} = \frac{p-r}{q-s}$, the process is called

The third proportional to $\displaystyle 15$ and $\displaystyle 20$ is

The third proportional to $\displaystyle 9$ and $\displaystyle 25$

If $\displaystyle A:B=5:3$, $\displaystyle B:C=6:7$ and $\displaystyle C:D=14:9$ then the value of $\displaystyle A:B:C:D$

The ratio compounded of $\displaystyle 4:5$ and sub-duplicate of $\displaystyle A:9$ is $\displaystyle 8:15$. Then value of "$\displaystyle A$" is

If $\displaystyle \frac{3x-2}{5x-6}$ is the duplicate ratio of $\displaystyle 2/3$ then the value of '$\displaystyle x$' is

If $\displaystyle x:y = 2:3$, then $\displaystyle (5x+2y):(3x-y) =$

A person has asset worth of $\displaystyle \text{Rs.} 1,48,200$. He wish to divide it amongst his wife, son and daughter in the ratio $\displaystyle 3:2:1$ respectively. From this assets share of his son will be.

$\displaystyle X, Y, Z$ together starts a business, if $\displaystyle X$ invests $\displaystyle 3$ times as much as $\displaystyle Y$ invests and $\displaystyle Y$ invests two third of what $\displaystyle Z$ invests, then the ratio of capitals of $\displaystyle X, Y, Z$ is

A bag contains $\displaystyle 25$ paise, $\displaystyle 10$ paise, and $\displaystyle 5$ paise in a ratio of $\displaystyle 3:2:1$. The total value of $\displaystyle \text{Rs.} 40$, the number of $\displaystyle 5$ paise coins is

What must be added to each term of the ratio $\displaystyle 49:68$. So that it becomes $\displaystyle 3:4$?

The difference of two numbers are $\displaystyle 3$. $\displaystyle 4$. The difference of their squares is $\displaystyle 28$. Greater number is:

The price of scooter and moped are in the ratio $\displaystyle 7:9$. The price of moped is $\displaystyle \text{Rs.} 1600$ more than that of scooter. Then the price of moped is:

Four persons $\displaystyle A, B, C, D$ wish to share a sum in the ratio of $\displaystyle 5:2:4:3$. If $\displaystyle D$ gets $\displaystyle \text{Rs.} 1000$ less than $\displaystyle C$, then the share of $\displaystyle B$?

The monthly incomes of $\displaystyle A$ & $\displaystyle B$ are in the ratio $\displaystyle 4:5$ are their monthly expenditures are in the ratio $\displaystyle 5:7$. If each saves $\displaystyle \text{Rs.} 150$ per month, find their monthly incomes.

Two vessels containing water and milk in the ratio $\displaystyle 2:3$ and $\displaystyle 4:5$ are mixed in the ratio $\displaystyle 1:2$. The ratio of milk and water in the resulting mixture is:

If $\displaystyle (x-9):(3x+6)$ is the duplicate ratio of $\displaystyle 4:9$, find the value of $\displaystyle x$.

If $\displaystyle \frac{a}{b} = \frac{c}{d} = \frac{2a+3b+2c}{4a-b+2c}$, then $\displaystyle \frac{a}{b}$ is

Which of the numbers are not in proportions?

If $\displaystyle A:B = 2:5$, then $\displaystyle (10A+3B):(5A+2B)$ is equal to

Value of $\displaystyle \frac{2^n + 2^{n-1}}{2^{n+1} - 2^n}$

Value of $\displaystyle \frac{2^{m+1} \times 3^{2m-n+3} \times 5^{n+m+4} \times 6^{2n+m}}{6^{2m+n} \times 10^{n+1} \times 15^{m+3}}$

Value of $\displaystyle \left[9^{n+\frac{1}{4}} \cdot \frac{\sqrt{3 \cdot 3^n}}{3 \cdot \sqrt{3^{-n}}}\right]^{\frac{1}{n}}$

If $\displaystyle X = \sqrt{3} + \frac{1}{\sqrt{3}}$, find the value of: $\displaystyle \left(X - \frac{\sqrt{126}}{\sqrt{42}}\right) \left(X - \frac{1}{X - \frac{2\sqrt{3}}{3}}\right)$

$\displaystyle \text{Find the value of } a \text{ from the following:} \\ \sqrt{(9)}^{-5} \times \sqrt{(3)}^{-7} = \sqrt{(3)}^{-a}$

Find the value of $\displaystyle 3t^{-1} / t^{-1/3}$

Let $\displaystyle a = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ and $\displaystyle b = \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$. What is the value of $\displaystyle a^2+b^2$?

The value of $\displaystyle \frac{6^{n+4}+3^{n+3} \times 2^{n+3}}{5 \times 6^n+6^n}$ is

If $\displaystyle \left(\frac{3a}{2b}\right)^{2x-4} = \left(\frac{2b}{3a}\right)^{2x-4}$, for some $\displaystyle a$ and $\displaystyle b$, then the value of $\displaystyle x$ is

If $\displaystyle (\sqrt{3})^{18} = (\sqrt{9})^x$, find $\displaystyle x$?

If $\displaystyle xy + yz + zx = -1$ then the value of $\displaystyle \left(\frac{x+y}{1+xy} + \frac{z+y}{1+zy} + \frac{x+z}{1+zx}\right)$ is:

The value of $\displaystyle \left(1-\sqrt[3]{0.027}\left(\frac{5}{6}\right)\left(\frac{1}{2}\right)^2\right)$ is

A sum of money is to be distributed among $\displaystyle A, B, C, D$ in the proportion of $\displaystyle 5:2:4:3$. If $\displaystyle C$ gets $\displaystyle ₹1000$ more than $\displaystyle D$, what is $\displaystyle B$'s share?

The mean proportional between $\displaystyle 12x^2$ and $\displaystyle 27y^2$

The monthly income of $\displaystyle A$ & $\displaystyle B$ are in the ratio $\displaystyle 4:5$ are their monthly expenditures are in the ratio $\displaystyle 5:7$. If each saves $\displaystyle ₹150$ per month, find their monthly incomes.

What is the value of $\displaystyle \frac{p+q}{p-q}$ if $\displaystyle \frac{p}{q} = \frac{7}{3}$?

If $\displaystyle x/2 = y/3 = z/7$, then the value of $\displaystyle (2x-5y+4z)/2y$ is

If four numbers $\displaystyle 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{5}$ are proportional then $\displaystyle x=$

A box contains $\displaystyle 276$ coins of $\displaystyle 5$ rupees, $\displaystyle 2$ rupees and $\displaystyle 1$ rupee. The value of each kind of coins are in the ratio $\displaystyle 2:3:5$ respectively. The number of $\displaystyle 2$ rupees coin is

What must be added to each term of the ratio $\displaystyle 49:68$, so that it becomes $\displaystyle 3:4$?

The students in three classes are in the ratio $\displaystyle 2:3:5$. If $\displaystyle 40$ students are increased in each class the ratio changes to $\displaystyle 4:5:7$. Originally the total number of students was

A bag contains coins of denominations $\displaystyle 1$ rupee, $\displaystyle 2$ rupee and $\displaystyle 5$ rupees. Their numbers are in the ratio $\displaystyle 4:3:2$. If bag has total of Rs. $\displaystyle 1800$ then find the number of $\displaystyle 2$ rupee coins.

The expenditures and savings of a person are in the ratio $\displaystyle 4:1$. If his savings are increased by $\displaystyle 25\%$ of his income, then what is the new ratio of his expenditure and savings ?

$\displaystyle P, Q$ and $\displaystyle R$ three cities. The ratio of average temperature $\displaystyle P$ and $\displaystyle Q$ is $\displaystyle 11:12$ and that between $\displaystyle P$ and $\displaystyle R$ is $\displaystyle 9:8$. The ratio between the average temperature $\displaystyle Q$ and $\displaystyle R$.

If $\displaystyle 1/2, 1/3, 1/5$ and $\displaystyle 1/x$ are in proportion, then the value of $\displaystyle x$ will be

The ratio of number of boys and number of girls in a school is found to be $\displaystyle 15:32$. How many boys and equal number of girls should be added to bring the ratio to $\displaystyle 2/3$?

If $\displaystyle P = x^{1/3} + x^{-1/3}$ then $\displaystyle P^3 - 3P =$

If $\displaystyle \sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}=0$ then the value of $\displaystyle \left(\frac{a+b+c}{3}\right)^3$ is equal to

If $\displaystyle x=y^a, y=z^b, z=x^c$, then the value of $\displaystyle abc$ is

If $\displaystyle \frac{9^n \times 3^5 \times (27)^5}{3 \times (81)^4} = 27$, then the value of $\displaystyle n$ is

What is the value of $\displaystyle \left(\frac{x^b}{x^c}\right)^{(b+c-a)} \times \left(\frac{x^c}{x^a}\right)^{(c+a-b)} \times \left(\frac{x^a}{x^b}\right)^{(a+b-c)}$

$\displaystyle x = \sqrt{\sqrt{6} + 6 + \left( \sqrt{7 + 2\sqrt{6}} \right)} - \sqrt{6}$ then the value of $\displaystyle x$ is

If $\displaystyle 2^x = 3^y = 6^z$ then $\displaystyle \frac{1}{x} + \frac{1}{y} =$

$\displaystyle 5^{16} + 125^5$ is divisible by which of the following

If $\displaystyle pqr = a^x$, $\displaystyle qrs = a^y$ and $\displaystyle rsp = a^z$, then find the value of $\displaystyle (pqrs)^{1/2}$

$\displaystyle \left( \frac{\sqrt{3}}{9} \right)^{5/2} \left( \frac{9}{3\sqrt{3}} \right)^{7/2} \times 9$ is equal to

Find the value of $\displaystyle \sqrt{6561} + \sqrt[4]{6561} + \sqrt[8]{6561}$

If $\displaystyle \frac{8^n \times 2^3 \times 16^{-1}}{2^n \times 4^2} = \frac{1}{4}$ then the value of $\displaystyle n$ is:

Simplify $\displaystyle \frac{2^{n} + 2^{n-1}}{2^{n+1} - 2^{n}}$

If $\displaystyle 2^a = 3^b = 12^c$ then $\displaystyle \frac{1}{a} + \frac{1}{b} =$

If $\displaystyle 3^x = 5^y = 75^z$ then $\displaystyle x+y-z = 0$

If $\displaystyle (25)^{150} = (25x)^{50}$; then the value of $\displaystyle x$ will be:

The value of $\displaystyle \frac{(3^{n+1} + 3^{n-1})}{(3^{n+3} - 3^{n+1})}$ is equal to

The value of $\displaystyle \frac{x^2 - (y - z)^2}{(x + z)^2 - y^2} + \frac{y^2 - (x - z)^2}{(x + y)^2 - z^2} + \frac{z^2 - (x - y)^2}{(y + z)^2 - x^2}$ is

If $\displaystyle abc = 2$ then the value of $\displaystyle \frac{1}{1+a+2b^{-1}} + \frac{1}{1+\frac{1}{2}b+c^{-1}} + \frac{1}{1+c+a^{-1}}$ is

Find the value of $\displaystyle \frac{3t^{-1}}{t^{-\frac{1}{3}}}$

The Value of $\displaystyle \left[ 9^{n + \frac{1}{4}} \cdot \frac{\sqrt{3 \cdot 3^n}}{3 \cdot \sqrt{3^{-n}}} \right]^{\frac{1}{n}}$ is?

If $\displaystyle 2^x \times 3^y \times 5^z = 720$ then the value of $\displaystyle x, y, z$ is

The Value of $\displaystyle \frac{2^{n+2} - 2^{n+1}}{2^{n+1} - 2^n}$ is

If $\displaystyle P = x^{1/3} + x^{-1/3}$ then find value of $\displaystyle 3P^3 - 9P$

If $\displaystyle (25)^{150} = (25x)^{50}$, then the value of $\displaystyle x$ will be:

The value of $\displaystyle \frac{64(b^4 a^3)^6}{\left[ 4(a^3 b)^2 \times (ab)^2 \right]}$

Value of $\displaystyle \left( a^{1/8} + a^{-1/8} \right) \left( a^{1/8} - a^{-1/8} \right) \left( a^{1/4} + a^{-1/4} \right) \left( a^{1/2} + a^{-1/2} \right)$ is:

If $\displaystyle (25)^{150} = (25x)^{50}$ then the value of $\displaystyle x$ will be

If $\displaystyle x:y = 3:4$, the value of $\displaystyle x^2y + xy^2 : x^3 + y^3$ is

If $\displaystyle a^x = b, b^y = c, c^z = a$, then $\displaystyle xyz$ is

The value of $\displaystyle \left( \frac{x^{a}}{x^{b}} \right)^{a^2+ab+b^2} \times \left( \frac{x^{b}}{x^{c}} \right)^{b^2+bc+c^2} \times \left( \frac{x^{c}}{x^{a}} \right)^{c^2+ac+a^2}$ is

If $\displaystyle p = x^{1/3} + x^{-1/3}$, then find value of $\displaystyle 3p^3 - 9p$

The value of the expression: $\displaystyle a^{\log_a b \cdot \log_b c \cdot \log_c d \cdot \log_d t}$ is?

The value of $\displaystyle \log_4 9 \cdot \log_3 2$ is

$\displaystyle \log_2 \log_2 \log_2 16 = ?$

$\displaystyle \log_{10} 0.0001 = ?$

If $\displaystyle \log_x \sqrt{3} = \frac{1}{6}$ find the value of $\displaystyle a$:

$\displaystyle \log 9 + \log 5$ is expressed as:

If $\displaystyle \log (ab) = x$, then $\displaystyle \log (\frac{a}{b})$ is

If $\displaystyle \log_{10} 3 = x$ and $\displaystyle \log_{10} 4 = y$, then the value of $\displaystyle \log_{10} 120$ can be expressed as

Find the value of $\displaystyle \log (x^2)$, if $\displaystyle \log (x) + 2\log (x^2) + 3\log (x^3) = 14$

If $\displaystyle \log_{10} 2 = y$ and $\displaystyle \log_{10} 3 = x$, then the value of $\displaystyle \log_{10} 15$ is:

$\displaystyle \log^2 x^3 - \log^2 x^2 - \log^2 x^0$ equal to:

The value of $\displaystyle [\log_{10} (5 \log_{10} 100)]^2$ is:

Given that $\displaystyle \log_x m = n - 1$ and $\displaystyle \log_{10} y = m - n$, the value of $\displaystyle \log_{10} (100x / y^2)$ is expressed in terms of $\displaystyle m$ and $\displaystyle n$ as

If $\displaystyle \log_a h = 3$ and $\displaystyle \log_c e = 2$, then $\displaystyle \log_c h$ is:

$\displaystyle \log_3 \log_3 \log_3 256 + 2\log_3 2$ is equal to:

The value of $\displaystyle \log_{0.1} 0.001$

If $\displaystyle \log_x 4 = -\frac{3}{2}$ then $\displaystyle x$ is

If $\displaystyle \log_x \log_{\sqrt{x}} (\sqrt{x} + \sqrt{x} + \sqrt{x}) = 0$ the value of $\displaystyle x$ is

If $\displaystyle a = \log_{24} 12$, $\displaystyle b = \log_{36} 24$, $\displaystyle \log_{48} 36$ then prove that $\displaystyle 1 + abc =$

If $\displaystyle \log_x s + \log_x x = \frac{3}{2}$ then $\displaystyle x$ is.

Given that $\displaystyle \log_x 2 = x$ and $\displaystyle \log_x 3 = y$, the value of $\displaystyle \log_x 60$ is expressed as

$\displaystyle \log_x x + \log(1 + x) = 0$ is equivalent to

The Value $\displaystyle \frac{\log_b 8}{\log_{16} 10 \cdot \log_4 10}$ is

If $\displaystyle \log_{10} 5 + \log_{10} (5x + 1) = \log_{10} (x + 5) + 1$, then $\displaystyle x$ is equal to

Find the value of $\displaystyle \log_y x^n + \log_x y^n + \log_n n^x$

$\displaystyle (18)^{3.5} \div (27)^{3.5} \times 6^{3.5} = 2^x$, then the value of $\displaystyle x$ is:

The value of $\displaystyle \frac{(243)^{0.13} \times (243)^{0.07}}{(7)^{0.25} \times (49)^{0.075} \times (343)^{0.2}}$ is:

The number of prime factors in $\displaystyle \frac{6^{12} \times (35)^{28} \times (15)^{16}}{(14)^{12} \times (21)^{11}}$ is :

The value of $\displaystyle \log_{64} 512$ is

The value of $\displaystyle (\log_b a \cdot \log_c b \cdot \log_a c)^3 =$

If $\displaystyle x^2 + y^2 = 7xy$, then $\displaystyle \log \frac{1}{3} (x + y)$ then $\displaystyle x$ is

Find the value of $\displaystyle \log_{10} \left[ 25 - \log_{10} (2)^3 + \log_{10} (4)^3 \right]$

If $\displaystyle x = \log_{24} 12$, $\displaystyle y = \log_{36} 24$, $\displaystyle z = \log_{48} 36$, then $\displaystyle xyz + 1 =$

The value of $\displaystyle \log_5 \left(1 + \frac{1}{5}\right) + \log_5 \left(1 + \frac{1}{6}\right) + \dots + \log_5 \left(1 + \frac{1}{624}\right)$

$\displaystyle \log_{\sqrt{3}} (512) : \log_{\sqrt{3}} 324 =$

If $\displaystyle \log x + \log 16 + \log x + \log 256 = \frac{25}{6}$ then the value of $\displaystyle x$ is

$\displaystyle \log \frac{p^2}{qr} + \log \frac{q^2}{pr} + \log \frac{r^2}{pq}$ is:

$\displaystyle \log \sqrt{3} = 6^{-1}$ base $\displaystyle a$, then '$\displaystyle a$' will be:

$\displaystyle \log_x 64 = 4$ is equal to:

$\displaystyle \frac{p^2 - q^2}{pr - qr} + \log \frac{r^2}{pq} =$

$\displaystyle \log_{0.001} 10000 = ?$

If $\displaystyle \frac{1}{2} \log_{10} 4 = y$ and if $\displaystyle \frac{1}{2} \log_{10} 9 = x$, then the value of $\displaystyle \log_{10} 15$

$\displaystyle 7 \log \frac{16}{15} + 5 \log \frac{25}{24} + 3 \log \frac{81}{80}$ is equal

If $\displaystyle \log_x (x^2 + x) - \log_x (x + 1) = 2$ find $\displaystyle x$

Given $\displaystyle \log 2 = 0.3010$ and $\displaystyle \log 3 = 0.4771$ then the value of $\displaystyle \log 24$

Given that $\displaystyle \log_{10} 2 = x$ and $\displaystyle \log_{10} 3 = y$ the value of $\displaystyle \log_{10} 120$ is expressed as

The simplified value of $\displaystyle 2 \log_{10} 5 + \log_{10} 8 - \frac{1}{2} \log_{10} 4$ is

If $\displaystyle \log \left( \frac{a + b}{4} \right) = \frac{1}{2} (\log a + \log b)$ then

On solving the equation $\displaystyle \log_x (1 + \log_x (1 - x)) = 1$ we get the value of $\displaystyle x$ as

If $\displaystyle \log 2 = 0.3010$ and $\displaystyle \log 3 = 0.4771$, then the value of $\displaystyle \log 24$ is:

If $\displaystyle \log (x^2 + x) - \log_x (x + 1) = 2$ then the value of $\displaystyle x$ is

If $\displaystyle a - b = \frac{1}{2} (\log a + \log b)$, the value of $\displaystyle a^2 + b^2$ is

If $\displaystyle \log_4 x = -3/2$ Then $\displaystyle x$ is

Given that $\displaystyle \log_{10} 2 = x$ and $\displaystyle \log_{10} 3 = y$, the value of $\displaystyle \log_{10} 120$ is expressed as

$\displaystyle \log \frac{a^2}{bc} + \log \frac{b^2}{ca} + \log \frac{c^2}{ab} =$

$\displaystyle \frac{1}{1 + \log_x yz} + \frac{1}{1 + \log_y zx} + \frac{1}{1 + \log_z xy} =$

If $\displaystyle n = m!$ where ($\displaystyle 'm'$ is a positive integer $\displaystyle > 2$) then the value of: $\displaystyle \frac{1}{\log_2 n} + \frac{1}{\log_3 n} + \frac{1}{\log_4 n} + \dots + \frac{1}{\log_m n}$

If $\displaystyle 2^x = 4^y = 8^z$ and $\displaystyle \frac{1}{2x} + \frac{1}{4y} + \frac{1}{6z} = \frac{24}{7}$, then the value of $\displaystyle z$ is:

Suppose a father had a sum of ₹ 3,600 and he decided to divide this amount among his three sons Anil, Sunil and Nimal in such a way that 3 times Anil's share, 6 times Sunil's share, and 8 times Nimal's share are all equal. Then Anil's share is

The ratio of age of two sisters is 5 : 7. One is elder to the other by 8 years. Then the ratio of their age after 4 years between older to younger is

If $\displaystyle \left(\frac{x}{y}\right)^{a^2+4} = (x^{-1}y)^{-5a}$ then the value of a is

If $\displaystyle x = \sqrt{2} + \frac{1}{\sqrt{2}}$ and $\displaystyle y = \sqrt{2} - \frac{1}{\sqrt{2}}$ then $\displaystyle x^2 + y^2$ is

The simplified value of $\displaystyle [5a^5b^2 \times 3(a b^3)^2] / (15a^2b)$ is

Three Employees A, B and C of a firm receive variable incentive money in the ratio 3 : 4 : 5. Then the Management also gave a fixed incentive of ₹ 4,000 to each of them. As a result now the total incentive amount of A, B and C becomes in the ratio 5 : 6 : 7. How much amount did B get as variable incentive?

The value of $\displaystyle x$ in $\displaystyle \log_x(4) + \log_x(16) + \log_x(64) = 12$ is

The value of $\displaystyle \left(\frac{y^a}{y^b}\right)^{a^2+ab+b^2} \times \left(\frac{y^b}{y^c}\right)^{b^2+bc+c^2} \times \left(\frac{y^c}{y^a}\right)^{c^2+ca+a^2}$ is equal to ?

A bag contains $\displaystyle 23$ number of coins in the form of $\displaystyle 1$ rupee, $\displaystyle 2$ rupee and $\displaystyle 5$ rupee coins. The total sum of the coins is $\displaystyle ₹43$. The ratio between $\displaystyle 1$ rupee and $\displaystyle 2$ rupees coins is $\displaystyle 3:2$. Then the number of $\displaystyle 1$ rupee coins.

The ratio of income of A and B is $\displaystyle 5:4$ and their expenditure is $\displaystyle 3:2$. If at the end of the year each saves $\displaystyle ₹1,600$, then the income of A is:

If $\displaystyle x = 2 + \sqrt{3}$ and $\displaystyle y = 2 - \sqrt{3}$ then value of $\displaystyle x^2 + y^2 =$

The ratio of the earnings of two persons $\displaystyle 3:2$. If each saves $\displaystyle 1/5^{th}$ of their earning, the ratio of their saving

If $\displaystyle a:b = 3:4$, the value of $\displaystyle (2a+3b):(3a+4b)$ is

If $\displaystyle x:y = 2:3$, then find $\displaystyle (5x-2y):(3x-y)$

The ratio of the speed of the two trains is $\displaystyle 2:5$. If the distances they travel are in the ratio $\displaystyle 5:9$, find the ratio of times taken by them.

Two nos. are in the ratio $\displaystyle 7:8$. If $\displaystyle 3$ is added to each of them, ratio becomes $\displaystyle 8:9$, the no. are