# How do you solve e^(-0.005x) = 100 ?

Apr 17, 2018

$\textcolor{b l u e}{x = - \ln \frac{100}{0.005} \approx - 921.0340372}$

#### Explanation:

By the laws of logarithms:

${\log}_{a} \left({b}^{c}\right) = c {\log}_{a} \left(b\right)$

${\log}_{a} \left(a\right) = 1$

${e}^{- 0 , 005 x} = 100$

Taking natural logarithms of both sides:

$- 0.005 x \ln \left(e\right) = \ln \left(100\right)$

From above:

$- 0.005 x = \ln \left(100\right)$

$\textcolor{b l u e}{x = - \ln \frac{100}{0.005} \approx - 921.0340372}$