Precalculus Examples

$\log_{4} (\frac{x + 9}{x}) = 4$

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, $b = 4$ , $x = \frac{x + 9}{x}$ , and $y = 4$ .

$b = 4$

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

$y = 4$

Step 2

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

$4^{4} = \frac{x + 9}{x}$