Top 39 CAT Logarithms, Surds and Indices Questions With Solutions

If $$(\sqrt{\frac{7}{5}})^{3x-y}=\frac{875}{2401}$$ and $$(\frac{4a}{b})^{6x-y}=(\frac{2a}{b})^{y-6x}$$, for all non-zero real values of a and b, then the value of $$x+y$$ is

For a real number a, if $$\frac{\log_{15}{a}+\log_{32}{a}}{(\log_{15}{a})(\log_{32}{a})}=4$$ then a must lie in the range

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals

If $$5 - \log_{10}\sqrt{1 + x} + 4 \log_{10} \sqrt{1 - x} = \log_{10} \frac{1}{\sqrt{1 - x^2}}$$, then 100x equals

If Y is a negative number such that $$2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$$, then Y equals to:

If $$\log_{a}{30}=A,\log_{a}({\frac{5}{3}})=-B$$ and $$\log_2{a}=\frac{1}{3}$$, then $$\log_3{a}$$ equals

The value of $$\log_{a}({\frac{a}{b}})+\log_{b}({\frac{b}{a}})$$, for $$1<a\leq b$$ cannot be equal to

If a,b,c are non-zero and $$14^a=36^b=84^c$$, then $$6b(\frac{1}{c}-\frac{1}{a})$$ is equal to

If $$x=(4096)^{7+4\sqrt{3}}$$, then which of the following equals to 64?

If $$\log_{4}{5}=(\log_{4}{y})(\log_{6}{\sqrt{5}})$$, then y equals

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals

If $$(5.55)^x = (0.555)^y = 1000$$, then the value of $$\frac{1}{x} - \frac{1}{y}$$ is

The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is

If m and n are integers such that $$(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})$$ then m is

Let x and y be positive real numbers such that
$$\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3,$$ and $$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$$. Then $$xy$$ equals

If x is a positive quantity such that $$2^{x}=3^{\log_{5}{2}}$$. then x is equal to

If $$\log_{12}{81}=p$$, then $$3(\dfrac{4-p}{4+p})$$ is equal to

If N and x are positive integers such that $$N^{N}$$ = $$2^{160}\ and \ N{^2} + 2^{N}\ $$ is an integral multiple of $$\ 2^{x}$$, then the largest possible x is

$$\frac{1}{log_{2}100}-\frac{1}{log_{4}100}+\frac{1}{log_{5}100}-\frac{1}{log_{10}100}+\frac{1}{log_{20}100}-\frac{1}{log_{25}100}+\frac{1}{log_{50}100}$$=?

If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to

Given that $$x^{2018}y^{2017}=\frac{1}{2}$$, and $$x^{2016}y^{2019}=8$$, then value of $$x^{2}+y^{3}$$ is

If $$\log_{2}({5+\log_{3}{a}})=3$$ and $$\log_{5}({4a+12+\log_{2}{b}})=3$$, then a + b is equal to

Suppose, $$\log_3 x = \log_{12} y = a$$, where $$x, y$$ are positive numbers. If $$G$$ is the geometric mean of x and y, and $$\log_6 G$$ is equal to

If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?

The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to

If $$9^{2x-1}-81^{x-1}=1944$$, then $$x$$ is

If $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$, then $$x$$ is

If $$log(2^{a}\times3^{b}\times5^{c} )$$is the arithmetic mean of $$log ( 2^{2}\times3^{3}\times5)$$, $$log(2^{6}\times3\times5^{7} )$$, and $$log(2 \times3^{2}\times5^{4} )$$, then a equals

If $$log_y x = (a*log_z y) = (b*log_x z) = ab$$, then which of the following pairs of values for (a, b) is not possible?

If x = -0.5, then which of the following has the smallest value?

Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?

If x >= y and y > 1, then the value of the expression $$log_x (x/y) + log_y (y/x)$$ can never be

Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has

If $$log_3 2, log_3 (2^x - 5), log_3 (2^x - 7/2)$$ are in arithmetic progression, then the value of x is equal to

If $$f(x) = \log \frac{(1+x)}{(1-x)}$$, then f(x) + f(y) is

If $$\log_{2}{\log_{7}{(x^2 - x+37)}}$$ = 1, then what could be the value of ‘x’?

Which of the following is true?

Find the value of $$\frac{1}{1 + \frac{1}{3-\frac{4}{2+\frac{1}{3-\frac{1}{2}}}}}$$ + $$\frac{3}{3 - \frac{4}{3+\frac{1}{2-\frac{1}{2}}}}$$

$$2^{73}-2^{72}-2^{71}$$ is the same as