# How do you solve 7*e^(x-3)=57?

Oct 27, 2016

#### Answer:

$x = 5.097141119$

$x = 5.1$

#### Explanation:

We start by rearranging to have ${e}^{x - 3}$ by its self.

$7 \cdot {e}^{x - 3} = 57$

${e}^{x - 3} = \frac{57}{7}$

the inverse function of e^x is ln(x) thus,

$\ln \left({e}^{x - 3}\right) = x - 3$

so,

$x - 3 = \ln \left(\frac{57}{7}\right)$

$x = \ln \left(\frac{57}{7}\right) + 3$

$x = \ln \left(57\right) - \ln \left(7\right) + 3$

$x = 5.097141119$

$x = 5.1$

so to check,

$7 \cdot {e}^{5.097141119 - 3}$

$= 57$