Question

If $\log \left(\frac{a+b}{3}\right)=\frac{1}{2}(\log a+\log b)$

• A. $a^2+b^2=3ab$
• B. $a^2+b^2=7ab$
• C. $a^2+b^2=ab$
• D. $a^2+b^2=-ab$

Answer 1

The correct option is B $a^2+b^2=7ab$

$\log \left(\frac{a+b}{3}\right)=\frac{1}{2}(\log a+\log b)$
$\therefore \log \left(\frac{a+b}{3}\right)=\log (ab{)}^{\frac{1}{2}}$
or $\frac{a+b}{3}=(ab{)}^{\frac{1}{2}}$
or $(a+b{)}^2=9ab$
$\Rightarrow a^2+b^2=7ab$