Precalculus Examples

$9 \ln (x - 6) = 1$

Step 1

Divide both sides by $9$ to remove it from the front of the logarithm.

$\frac{9 \ln (x - 6)}{9} = \frac{1}{9}$

Step 2

Simplify each side of the equation.

$\ln (x - 6) = \frac{1}{9}$

Step 3

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, $b = e$ , $x = x - 6$ , and $y = \frac{1}{9}$ .

$b = e$

$x = x - 6$

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

Step 4

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

$e^{\frac{1}{9}} = x - 6$