IPMAT Indore 2024 (MCQ) - If _4 x = a and _25 x = b, then _x 10 is | PYQs + Solutions

IPMAT Indore 2024

Modern Math

Logarithms

Medium

If $\log_4 x = a$ and $\log_{25} x = b$ , then $\log_x 10$ is

\dfrac{a + b}{2}

\dfrac{a - b}{2ab}

\dfrac{a + b}{2ab}

\dfrac{a + b}{2(a - b)}

Correct Option: 3

Property:

\log_{a^b} c^d = \frac db \log_a c

\newline

Thus,

\boxed{\log_{4} x = \log_{2^2} x = \frac 12 \log_2 x}

and

\boxed{\log_{25} x = \log_{5^2} x = \frac 12 \log_5 x}