Precalculus Examples

$y = \ln ({(| \frac{x^{2} - x - 12}{{(x + 6)}^{5}} |)}^{\frac{1}{4}})$

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, $b = e$ , $x = {(| \frac{x^{2} - x - 12}{{(x + 6)}^{5}} |)}^{\frac{1}{4}}$ , and $y = y$ .

$b = e$

$x = {(| \frac{x^{2} - x - 12}{{(x + 6)}^{5}} |)}^{\frac{1}{4}}$

$y = y$

Step 2

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

$e^{y} = {(| \frac{x^{2} - x - 12}{{(x + 6)}^{5}} |)}^{\frac{1}{4}}$