Precalculus Examples

$\ln ({(4)}^{x + 4}) = \ln ({(5)}^{x + 5})$

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, $b = e$ , $x = {(4)}^{x + 4}$ , and $y = \ln ({(5)}^{x + 5})$ .

$b = e$

$x = {(4)}^{x + 4}$

$y = \ln ({(5)}^{x + 5})$

Step 2

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

$e^{\ln ({(5)}^{x + 5})} = {(4)}^{x + 4}$