Solve for x log base 5 of x=-4

$\log_{5} (x) = - 4$

Rewrite $\log_{5} (x) = - 4$ 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 $b^{y} = x$ .

$5^{- 4} = x$

Solve for $x$

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Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

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

$\frac{1}{625} = x$

Rewrite the equation as $x = \frac{1}{625}$ .

$x = \frac{1}{625}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{625}$

Decimal Form:

$x = 0.0016$

Solve for x log base 5 of x=-4

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