Answer
$\frac{1}{2}$
Work Step by Step
Re-write $\sqrt[4]{25}=25^{\frac{1}{4}}$.
$x=\log_5{25}^{\frac{1}{4}}$
Write expression in exponential form.
$5^x=25^{\frac{1}{4}}$
Re-write both sides in terms of the same base.
$5^x=(5^2)^{\frac{1}{4}}$
Set exponents equal. (If $x^a=x^b$, then $a=b$.)
$x=2(\frac{1}{4})=\frac{1}{2}$
