NDA 2025 Maths · Mathematics · Logarithms · medium

/are correct (all logarithms defined, bases positive and not equal to 1)? 1. log ab·log bc=log ac 2. log (x+y)=log x+log y for all positive x,y

Single correct option

Which of the following statements is/are correct (all logarithms defined, bases positive and not equal to

1

)?
1.

\log_ab\cdot\log_bc=\log_ac

\log(x+y)=\log x+\log y

for all positive

x,y

Show answer and solution

Answer: (A) 1 only

Statement 1 is the chain (change of base) rule:

\frac{\log b}{\log a}\cdot\frac{\log c}{\log b}=\frac{\log c}{\log a}

. Statement 2 is false; the sum of logs is

\log(xy)

. For

x=y=1

\log2\ne0

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