# How to simplify this logarithm to find the value of x? [closed]

$$x^{log_2 x} = 2^4$$

Solve for x.

How to do this?

• Take $\log_2$ on both sides, for starters. – Teresa Lisbon Jan 19 at 9:30

By some easy algebraic computations, we get $$x^{\log_2x}=2^{\log_2(x^{\log_2x})}=2^{\log_2x \times \log_2x}=2^{\log_2^2x}$$.
$$\Rightarrow \log_2^2x = 4$$
$$\Rightarrow \log_2x = \pm 2$$
$$\Rightarrow x_1 = 2^2 = 4$$ and $$x_2 = 2^{-2} = \frac{1}{4}$$