NDA 2018 Maths · Mathematics · Logarithms · medium

Log (ab)=log a+log b for all non-zero real numbers a and b. 2. log a b·log b a=1 for a,b>0 and a,b≠1.

Single correct option

Consider the following statements: 1.

\log(ab)=\log a+\log b

for all non-zero real numbers

a

and

b

. 2.

\log_a b\cdot\log_b a=1

for

a,b>0

and

a,b\ne1

. Which of the statements given above is/are correct?

Show answer and solution

Answer: (B) 2 only

Statement 1 fails when

a,b

are both negative:

\log(ab)

exists but

\log a,\log b

do not, and the identity needs

a,b>0

. Statement 2 is true by the change of base formula:

\log_a b=\dfrac{1}{\log_b a}

. Only statement 2 is correct.

Original question written in the NDA 2018 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