Precalculus Examples

$g (\frac{1}{9}) = \log_{3} (\frac{1}{9})$

Step 1

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 3$ , $x = \frac{1}{9}$ , and $y = g (\frac{1}{9})$ .

$b = 3$

$x = \frac{1}{9}$

$y = g (\frac{1}{9})$

Step 2

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$3^{g (\frac{1}{9})} = \frac{1}{9}$