Question

How would is solve 5e^0.2x=7
Does it become 5^0.2x=ln7

Answer 1

\[ 5e^{0.2x}=7 \]
you could do this:
\[ \ln(5e^{0.2x}) = \ln(7) \]
but that is not the best thing. There are rules for tackling this , but it's easier if we do this instead:
\[ 5e^{0.2x}=7 \]
divide both sides by 5
\[ \frac{5}{5} e^{0.2x}= \frac{7}{5} \]
5/5 is 1 so the left side simplifies to
\[ e^{0.2x}= \frac{7}{5} \]

now write ln around each side