Precalculus Examples

$\log_{a} (2) = 5$

Step 1

Rewrite $\log_{a} (2) = 5$ 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 $b^{y} = x$ .

$a^{5} = 2$

Step 2

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

$a = \sqrt[5]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt[5]{2}$

Decimal Form:

$a = 1.14869835 \dots$