Question

solve the equation. give an exact solution, and also an app
$e^{4x}=8$
a. the exact solution is $x = \frac{\text{ln}(8)}{4}$.
b. the approximate solution is $x \approx$ (do not round until the final answer. then round to four decin

Explanation:

Step1: Take natural - log of both sides

$\ln(e^{4x})=\ln(8)$

Step2: Use log property $\ln(e^a)=a$

$4x = \ln(8)$

Step3: Solve for x

$x=\frac{\ln(8)}{4}$

Step4: Calculate the approximate value

$x=\frac{\ln(8)}{4}\approx\frac{2.079442}{4}\approx0.5199$

Answer:

a. $x = \frac{\ln(8)}{4}$
b. $x\approx0.5199$