Question

If $a^2+b^2=23ab$, then the value of $\left[\log \frac{a+b}{5}-\frac{1}{2}(\log a+\log b)\right]$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

$a^2+b^2+2ab=23ab+2ab{(a+b)}^2=25ab\text{taking square root}a+b=5\sqrt{ab}\text{Taking log}\log (a+b)=\log 5+\log \sqrt{ab}\log (a+b)-\log 5-\log \sqrt{ab}=0\log \left[\frac{(a+b)}{5}\right]-\frac{1}{2}\log ab=0\text{Applying multiplication property}\log \left[\frac{a+b}{5}\right]-\frac{1}{2}\left(\log \right(a)+\log (b\left)\right)=0$