Question

Solve for x. Round to the nearest hundredth. Show all work.

Answer 1

The equation is given as,

`3e^(5x)=1977`

Transpose the term,

`\begin{gathered} e^(5x)=(1977)/(3) \\ e^(5x)=659 \end{gathered}`

Taking logarithm on both sides,

`\ln (e^(5x))=\ln (659)`

Consider the formula,

`\ln (e^m)=e^(\ln (m))=m`

Applying the formula,

`\begin{gathered} 5x=\ln (659) \\ x=(1)/(5)\cdot\ln (659) \\ x\approx1.30 \end{gathered}`

Thus, the solution of the given exponential equation is approximately equal to,

`1.30`