Ratio, Proportion, Indices, Logarithm

$3x-2:5x+6$ the duplicate ratio of $2:3$ then find the value $x$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The sub-triplicate ratio of $8:27$

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

If the ratio of two numbers is $7:11$. If $7$ is added to each number then the new ratio will be $2:3$ then the numbers are.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The third proportional to $9$ and $25$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the numbers are not in proportions?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$ \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 $ \sqrt{6561} + \sqrt[4]{6561} + \sqrt[8]{6561} $

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

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

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

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

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

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

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

If $abc = 2$ then the value of $ \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 $\frac{3t^{-1}}{t^{-\frac{1}{3}}}$

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

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

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

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

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

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

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

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

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

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

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

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

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

$\log_2 \log_2 \log_2 16 = ?$

$\log_{10} 0.0001 = ?$

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

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

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

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

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

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

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

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

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

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

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

The value of $\log_{0.1} 0.001$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\log_x 64 = 4$ is equal to:

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

$\log_{0.001} 10000 = ?$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

If $p:q$ is the sub-duplicate ratio of $p-x^2:q-x^2$, then $x^2$ is

If $x:y=z:7=4:11$ then $\frac{x+y+z}{z}$ is

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

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

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

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

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

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

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

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

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

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

If $2^{x^2} = 3^{y^2} = 12^{z^2}$ then

By simplifying $(2a^3b^4)^6 / [(4a^3b)^2 \times (a^2b^2)]$, the answer will be:

Given $x = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ and $y = \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$. Then find the value of $\frac{1}{x^2} + \frac{1}{y^2}$.

Find the value of $(x + y)$, if $\left(x + \frac{y^3}{x^2}\right)^{-1} - \left(\frac{x^2}{y} + \frac{y^2}{x}\right)^{-1} + \left(\frac{x^3}{y^2} + y\right)^{-1} = \frac{1}{3}$

$\log_a \sqrt{3} - \frac{1}{6}$ find the value of $a$

If $\log_3 4 \cdot \log_4 5 \cdot \log_5 6 \cdot \log_6 7 \cdot \log_7 8 \cdot \log_8 9 = x$, then find the value of $x$