Solve for x log base x of 1/32=5

$\log_{x} (\frac{1}{32}) = 5$

Rewrite $\log_{x} (\frac{1}{32}) = 5$ 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 $b^{y} = x$ .

$x^{5} = \frac{1}{32}$

Solve for $x$ .

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[5]{\frac{1}{32}}$

Simplify $\sqrt[5]{\frac{1}{32}}$ .

Rewrite $\sqrt[5]{\frac{1}{32}}$ as $\frac{\sqrt[5]{1}}{\sqrt[5]{32}}$ .

$x = \frac{\sqrt[5]{1}}{\sqrt[5]{32}}$

Any root of $1$ is $1$ .

$x = \frac{1}{\sqrt[5]{32}}$

Simplify the denominator.

Rewrite $32$ as $2^{5}$ .

$x = \frac{1}{\sqrt[5]{2^{5}}}$

Pull terms out from under the radical, assuming real numbers.

$x = \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x log base x of 1/32=5

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