Precalculus Examples

$t = \frac{\ln (2)}{\ln (0.115)}$

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, $b = e$ , $x = 2$ , and $y = t$ .

$b = e$

$x = 2$

$y = t$

Step 2

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

$e^{t} = 2$