# How do you evaluate 5e^(3x+7)=21?

Mar 6, 2016

$x = \frac{\ln \left(\frac{21}{5}\right) - 7}{3} \approx - 1.8550$

#### Explanation:

Divide both sides by $5$.

${e}^{3 x + 7} = \frac{21}{5}$

To undo the exponential function with a base of $e$, take the logarithm of both sides with base $e$. Note that ${\log}_{e} \left(x\right)$ is the natural logarithm, denoted $\ln \left(x\right)$.

$\ln \left({e}^{3 x + 7}\right) = \ln \left(\frac{21}{5}\right)$

$3 x + 7 = \ln \left(\frac{21}{5}\right)$

Subtract $7$ from both sides.

$3 x = \ln \left(\frac{21}{5}\right) - 7$

Divide both sides by $3$.

$x = \frac{\ln \left(\frac{21}{5}\right) - 7}{3} \approx - 1.8550$