List of top Quantitative Aptitude Questions on Logarithms asked in CAT

\(\frac{2×4×8×16}{(log_24)^2(log_48)^3(log_816)^4}\) equals [This Question was asked as TITA]
If \(a, b, c\) are non-zero and \(14^a = 36^b = 84^c\), then \(6b \bigg(\frac{1}{c}-\frac{1}{a}\bigg)\)is equal to

\(\frac{2×4×8×16}{(log_24)^2(log_48)^3(log_816)^4}\) equals

If \(log_45=(log_4y)(log_6\sqrt5)\),then \(y\) equals
Let x and y be positive real numbers such that log5(x+y) + log5(x-y) = 3, and log2y - log2x = 1 - log23. Then xy equals
If log 2(5+log3a)=3 and log5(4a+12+log2b) = 3, then a+b is equal to
If x is a positive quantity such that 2x = 3log52, then x is equal to
If p3 = q 4 = r5 = s6 , then the value of logs(pqr) is equal to
1/log2100-1/log4100+1/log5100-1/log10100+1/log20100-1/log25100+1/log50100=?
log12 81=p, then 3(4-p/4+p) is equal to
If log (2a × 3b × 5C) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57 ), and log (2 × 32 × 54 ), then a equals
The value of \(\text {log}_{0.008}\sqrt{5}+\text{log}_{\sqrt{3}}81-7\) is equal to
If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?
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 $\log_2 x + \log_4 x = 5$, what is the value of $x$? 
 

If $\log_2 x + \log_4 x = 3$, find $x$.
Which of the terms \( 2^{1/3}, 3^{1/4}, 4^{1/6}, 6^{1/8}, 10^{1/12} \) is the largest?
If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)

If $\log_2 (x) + \log_4 (x) = 5$, what is $x$? 
 

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

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