# How do you simplify 5^(log_5x)?

Feb 13, 2017

See below.

#### Explanation:

Make $y = {5}^{{\log}_{5} x}$

Apply ${\log}_{5}$ to both sides

${\log}_{5} y = {\log}_{5} x {\log}_{5} 5 = {\log}_{5} x \cdot 1 = {\log}_{5} x$

Now ${\log}_{5} y = {\log}_{5} x \to y = x$ so

${5}^{{\log}_{5} x} = x$