# How do you solve e^(x+2) = 50?

Dec 29, 2016

$1.91 \left(3 s . f .\right)$

#### Explanation:

convert to logarithmic form:

${a}^{m} = n \to {\log}_{a} \left(n\right) = m$

${e}^{x + 2} = 50 \to {\log}_{e} \left(50\right) = x + 2$

${\log}_{e} \left(n\right)$ can also be written as $\ln \left(n\right)$.

$\therefore {\log}_{e} \left(50\right) = \ln \left(50\right)$

$= x + 2$

enter into a calculator:

$\ln \left(50\right) = 3.91202 . .$

$= 3.91 \left(3 s . f .\right)$

$x + 2 = 3.91 \left(3 s . f .\right)$

subtract 2:

$x = 1.91 \left(3 s . f .\right)$