List of top Quantitative Aptitude Questions on Logarithms asked in CAT

If \(a\), \(b\), and \(c\) are positive real numbers such that \(a > 10 \ge b \ge c\) and\[ \frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a-b)}{\log_3 c} = \frac{2}{3} \]then the greatest possible integer value of \(a\) is

Let $x$ be a positive real number such that $4 \log_{10} x + 4 \log_{100} x + 8 \log_{1000} x = 13$ , then the greatest integer not exceeding $x$. is

The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is

X is a +ve real no, 4 log₁₀ (x) + 4log ₁₀₀ (x) + 8 log₁₀₀₀ (x) = 13, then the greatest integer not exceeding 'x'

For a real number \(x\) , if \(\frac{1}{2},\frac{log_3(2^x-9)}{log_34}\), and \(\frac{log_5\bigg(2^x+\frac{17}{2}\bigg)}{log_54}\) are in an arithmetic progression, then the common difference is

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 \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals

The number of distinct integer values of n satisfying \(4−\log\frac{2n}{3}−\log4n\lt0\), is

If log2[3 + log3{4 + log4(x - 1)}] - 2 = 0 then 4x equals

If 5 - log10 root 1 + x + 4 log10 root 1-x = log10 1/ 1-x2, then 100 x equals

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  \(log_2[3 + log_ 3[4 + log_4(x - 1)] - 2 = 0\) 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 \(100 x \) equals

\(\frac{2×4×8×16}{(log_24)^2(log_48)^3(log_816)^4}\) equals [This Question was asked as TITA]

If \(log_45=(log_4y)(log_6\sqrt5)\),then \(y\) equals
[This Question was asked as TITA]

If \(log_a\) \(30\) = \(A\), \(log_a\) \(\bigg(\frac{5}{3}\bigg)\) = \(-B\) and \(log_2\; a\) = \(\frac{1}{3}\), then \(log_3\) \(a\) equals.

The value of \(log_a\bigg(\frac{a}{b}\bigg)+log_b\bigg(\frac{b}{a}\bigg)\), for \(1<a≤b\) cannot be equal to

If \(y\) is a negative number such that \(2^{y^2log_35 }\)= \(5^{log_23}\), then \(y\) equals

If \(log_45=(log_4y)(log_6\sqrt5)\),then \(y\) equals