Answer
$x = 5\ln{\frac{7}{5}}$
Work Step by Step
Divide both sides of the equation by 5 to obtain:
$\dfrac{5e^{0.2x}}{5} = \dfrac{7}{5} \\e^{0.2x}=\dfrac{7}{5}$
Take the natural logarithm of both sides to obtain: $\ln{e^{0.2x}} = \ln{\frac{7}{5}}$
Note that $\ln{e^x} = x$.
Thus, the equation above is equivalent to:
$0.2x = \ln{\frac{7}{5}}$
Divide by $0.2$ on both sides of the equation to obtain:
$\dfrac{0.2x}{2} = \dfrac{\ln{\frac{7}{5}}}{0.2}
\\x = \dfrac{\ln{1.4}}{0.2}$
Note that $0.2=\frac{1}{5}$. This means that the equation above is equivalent to:
$x=\dfrac{\ln{\frac{7}{5}}}{\frac{1}{5}}
\\x = (\ln{\frac{7}{5}}) \cdot \dfrac{5}{1}
\\x = 5\ln{\frac{7}{5}}$
