Precalculus Examples

$\log_{2} (x) = \log_{4} (36)$

Step 1

Rewrite $\log_{2} (x) = \log_{4} (36)$ 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 $b^{y} = x$ .

$2^{\log_{4} (36)} = x$

Step 2

Rewrite the equation as $x = 2^{\log_{4} (36)}$ .

$x = 2^{\log_{4} (36)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 2^{\log_{4} (36)}$

Decimal Form:

$x = 6$