# What is the solution to the equation e^(5-3x)=10?

Apr 22, 2018

$x = \frac{5 - \ln 10}{3}$

#### Explanation:

Apply the natural logarithm to both sides:

$\ln \left({e}^{5 - 3 x}\right) = \ln 10$

Recalling the exponent property for logarithms, which tells us that $\ln \left({a}^{b}\right) = b \ln a ,$ we rewrite as

$\left(5 - 3 x\right) \ln e = \ln 10$

$\ln e = 1 ,$ so we get

$5 - 3 x = \ln 10$

Solve for $x :$

$3 x = 5 - \ln 10$

$x = \frac{5 - \ln 10}{3}$