Question

If $a,b,c$ are three consecutive positive integers and $\log (1+ac)=2k,$ then the value of $k$ is

• A. $\log b$
• B. $\log a$
• C. $2$
• D. $1$

Answer 1

The correct option is A $\log b$

Let $a=n-1,b=n,c=n+1,$ where $n>1$
Given, $\log (1+ac)=2k$
$\Rightarrow \log (1+n^2-1)=2k$
$\Rightarrow 2\log n=2k$
$\Rightarrow \log n=k$
$\Rightarrow \log b=k$