Precalculus Examples

$\ln (x^{2} + x - 5) = 0$

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, $b = e$ , $x = x^{2} + x - 5$ , and $y = 0$ .

$b = e$

$x = x^{2} + x - 5$

$y = 0$

Step 2

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

$e^{0} = x^{2} + x - 5$