Question

3e^(5x-2) + 5 = 12

Answer 1

Solve for X

Answer 2

\[3e ^{5x-2}+5=12\] subtract 5 to both sides
\[3e ^{5x-2}=7\] divide by 3 to both sides
\[e ^{5x-2}=7/3\] Take the ln of both sides
\[ln(e ^{5x-2})=ln(7/3)\] drop the power (ln property)
\[(5x-2)ln(e)=ln(7/3)\] note lne=1
\[5x-2=ln(7/3)\] add 2 to both sides
\[5x=ln(7/3)+2\] divide 5 to both sides
\[x=(ln(7/3)+2)/5\]