Answer
$5\ln(1.4)$
Work Step by Step
Divide $5$ to both sides of the equation to obtain:
$5 e^{0.2x} =7$
$e^{0.2x}=\dfrac{7}{5}$
$e^{0.2x}=1.4$
$\because e^y=x \text{ is equivalent to } y=\ln{x}$
$\therefore e^{0.2x} = 1.4 \text{ is equivalent to } 0.2x=\ln{1.4}$
Solve the equation above by multiplying $5$ to both sides of the equation to obtain:
\begin{align*}
0.2x&=\ln{1.4}\\
5(0.2x&)=5(\ln{1.4})\\
x&=5\ln(1.4)
\end{align*}
