Question

The value of ${\log }_{5+2\sqrt{6}}(5-2\sqrt{6})$ is

• A. $1$
• B. $-1$
• C. $2$
• D. None of these

Answer 1

The correct option is B $-1$

Let $p=5+2\sqrt{6},q=5-2\sqrt{6}$
$\Rightarrow pq=1$
$\Rightarrow p=\frac{1}{q}$

$\therefore {\log }_{5+2\sqrt{6}}(5-2\sqrt{6})={\log }_p\frac{1}{p}=-1$