Precalculus Examples

$\log_{x} (\log_{0.25} (\frac{1}{16})) = 1$

Step 1

Rewrite $\log_{x} (\log_{0.25} (\frac{1}{16})) = 1$ 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 $b^{y} = x$ .

$x^{1} = \log_{0.25} (\frac{1}{16})$

Step 2

Simplify.

$x = \log_{0.25} (\frac{1}{16})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \log_{0.25} (\frac{1}{16})$

Decimal Form:

$x = 2$