CAT Logarithms Practice Questions With Solutions

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

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$. If $a^{m}b^{n}=144^{145}$, then the largest possible value of $n-m$ is

The sum of all possible values of x satisfying the equation $2^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=0$, is

For a real number x, if $\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$, and $\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$ are in an arithmetic progression, then the common difference 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 Y is a negative number such that $2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$, then Y equals to:

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

Let the m-th and n-th terms of a geometric progression be $\frac{3}{4}$ and 12. respectively, where $m < n$. If the common ratio of the progression is an integer r, then the smallest possible value of $r + n - m$ is

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

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