NDA 2016 Maths · Mathematics · Logarithms · easy

If log 102=a and log 103=b, then log 1072 is equal to

Single correct option

\log_{10}2=a

and

\log_{10}3=b

, then

\log_{10}72

is equal to

Show answer and solution

Answer: (D) $3a+2b$

Factorise

72=2^3\cdot3^2

. Then

\log_{10}72=3\log_{10}2+2\log_{10}3=3a+2b

. Swapping the exponents gives

2a+3b

, which corresponds to

2^2\cdot3^3=108

, and logarithms of a product add rather than multiply.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake