CAT Logarithms, Surds and Indices Questions With Video Solutions

If x is a positive real number such that $$x^8 + \left(\frac{1}{x}\right)^8 = 47$$, then the value of $$x^9 + \left(\frac{1}{x}\right)^9$$ is

If $$x$$ and $$y$$ are positive real numbers such that $$\log_{x}(x^2 + 12) = 4$$ and $$3 \log_{y} x = 1$$, then $$x + y $$ equals

If $$\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$$, then $$\sqrt{10x+9}$$ is equal to

For some positive real number x, if $$\log_{\sqrt{3}}{(x)}+\frac{\log_{x}{(25)}}{\log_{x}{(0.008)}}=\frac{16}{3}$$, then the value of $$\log_{3}({3x^{2}})$$ is

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