Precalculus Examples

$10 t = - \ln (1 - \frac{i}{0.3})$

Step 1

Multiply both sides by $- 1$ to remove the negative sign in front of the logarithm.

$- 10 t = \ln (1 - \frac{i}{0.3})$

Step 2

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, $b = e$ , $x = 1 - \frac{i}{0.3}$ , and $y = - 10 t$ .

$b = e$

$x = 1 - \frac{i}{0.3}$

$y = - 10 t$

Step 3

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

$e^{- 10 t} = 1 - \frac{i}{0.3}$