Dividing the given equation by 25 we get:
[tex]\begin{gathered} \frac{100}{25}=\frac{25e^{3x}}{25}, \\ 4=e^{3x}\text{.} \end{gathered}[/tex]
Applying the natural logarithm to the above equation we get:
[tex]\ln (4)=\ln (e^{3x})=3x\ln (e)=3x\text{.}[/tex]
Finally, solving for x we get:
[tex]x=\frac{\ln (4)}{3}\text{.}[/tex]
Answer: Option A.
