Precalculus Examples

$\log_{x} (5) = 3$

Step 1

Rewrite $\log_{x} (5) = 3$ 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 $b^{y} = x$ .

$x^{3} = 5$

Step 2

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

$x = \sqrt[3]{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[3]{5}$

Decimal Form:

$x = 1.70997594 \dots$