thanks i understand now, the answer is 2+ radical 5 rite?
$\displaystyle \displaystyle log_{\frac{1}{2+\sqrt{5}}}(-2+\sqrt{5})=x-4\Rightarrow \left(\frac{1}{2+\sqrt{5}}\right)^{x-4}=\sqrt{5}-2$
The answer is an integer.
To bring the x-4 down, you must take the log of both sides.
Hint: use $\displaystyle \displaystyle log_{\frac{1}{2+\sqrt{5}}$
Spoiler: