Question

The value of ${\log }_{2-\sqrt{3}}(2+\sqrt{3})=-x$. Then $x$ is:

Answer 1

Let $-x={\log }_{(2-\sqrt{3})}(2+\sqrt{3})$
$\Rightarrow (2-\sqrt{3}{)}^{-x}=2+\sqrt{3}$
$\Rightarrow (2-\sqrt{3}{)}^{-x}=\frac{(2+\sqrt{3})(2-\sqrt{3})}{2-\sqrt{3}}=(2-\sqrt{3}{)}^{-1}$
$\Rightarrow -x=-1$

$\therefore x=1$