Solve for x log base x of 5=1/4

$\log_{x} (5) = \frac{1}{4}$

Rewrite $\log_{x} (5) = \frac{1}{4}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ $\neq$ $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$x^{\frac{1}{4}} = 5$

Solve for $x$

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Remove parentheses.

$x^{\frac{1}{4}} = 5$

Raise each side of the equation to the $4$ power to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{4}})}^{4} = {(5)}^{4}$

Raise $5$ to the power of $4$ .

$x = 625$

Solve for x log base x of 5=1/4