Answer
(a) $x=\dfrac{\ln{8}}{0.4}$
(b) $x \approx 5.198604$
Work Step by Step
(a)
Take the natural logarithm of both sides to obtain:
$\ln{e^{0.4x}} = \ln{8}$
Use the rule $\ln{e^n} = n$ to obtain:
$0.4x = \ln{8}
\\\dfrac{0.4x}{0.4}=\dfrac{\ln{8}}{0.4}
\\x=\dfrac{\ln{8}}{0.4}$
(b) Use a calculator to evaluate the answer and have:
$x \approx 5.198604$
