Question

0.5e^0.08x=40

Answer 1

\[\large \frac{1}{2}e^{0.08x}=40\]Start by multiplying both sides by 2,\[\large \cancel{2}\cancel{\frac{1}{2}}e^{0.08x}=40(2)\]

Giving us,\[\large e^{0.08x}=80\]
Then we'll take the natural log of both sides,\[\large \ln\left(e^{\color{royalblue}{0.08x}}\right)=\ln(80)\]

Answer 2

The log allows us to get the x out of the exponent position.
Here is an important log rule,\[\large \log(a^{\color{orangered}{b}})=\color{orangered}{b}\log(a)\]

Answer 3

Applying this to our problem gives us,\[\large \color{royalblue}{0.08x}\ln\left(e\right)=\ln(80)\]

Answer 4

Then just do a few algebra steps to solve for x!