List of top Quantitative Ability and Data Interpretation Questions on Logarithms

Find log\(_{5}\)(125) + log\(_{2}\)(1/16)

If log\(_{10}\)(5) = a and log\(_{10}\)(3) = b, express log\(_{10}\)(75) in terms of a & b.

Consider the equation, \(log_5(x-2) = 2log_{25}(2x-4)\) where x is a real number.
For how many different values of x does the given equation hold?

Find the value of: $\log 87600+\log 23100-8 =\ ?$

Sham is trying to solve the expression:
\[ \log \tan 1^\circ + \log \tan 2^\circ + \log \tan 3^\circ + \ldots + \log \tan 89^\circ. \]  
The correct answer would be?

If \(\log_{10} 11 = a\) then \(\log_{10} \left(\frac{1}{110}\right)\) is equal to?

If \(\frac{1}{2}\log x + \frac{1}{2}\log y + \log 2 = \log(x+y)\), then:

\(\log_5 25 + \log_2(\log_3 81)\) is:

If \(\log(x^2y^4) = a\) and \(\log \frac{x}{y} = b\), find the value of \(\frac{\log x}{\log y}\).

Each of the following questions is followed by two statements, I and II. Answer as follows:
Mark option (1) if the question can be answered using statement I alone, but not using statement II alone.
Mark option (2) if the question can be answered using statement II alone, but not using statement I alone.
Mark option (3) if the question can be answered using both statements I and II together, but not by using either statement alone.
Mark option (4) if the question cannot be answered even using both statements I and II together.

What is the value of \(x\)?
I. \( \log_2 2^x = x \)
II. \( \log_3 x = 0 \)