Question

Solve : 5e^-x -7=2
Please Show Work !

Answer 1

\[5e^{-x}-7=2\] add \(7\) get
\[5e^{-x}=9\] divide by \(5\) and get
\[e^{-x}=\frac{9}{5}\]so the first two steps are familiar elementary algebra in "solving for \(x\)"

Answer 2

now comes the only non algebra step, rewrite in logarithmic form
\[e^{-x}=\frac{9}{5}\iff -x=\ln(\frac{9}{5})\]

Answer 3

and finally back to algebra
\[-x=\ln(\frac{9}{5})\iff x=-\ln(\frac{9}{5})\]

Answer 4

if you want to be fancy, you can write
\[-\ln(\frac{9}{5})=\ln(\frac{5}{9})\] or even
\[\ln(5)-\ln(9)\]

Answer 5

5e^-x=9
e^-x=9/5
x=In(5/9)