The equation is given as,
[tex]3e^{5x}=1977[/tex]
Transpose the term,
[tex]\begin{gathered} e^{5x}=\frac{1977}{3} \\ e^{5x}=659 \end{gathered}[/tex]
Taking logarithm on both sides,
[tex]\ln (e^{5x})=\ln (659)[/tex]
Consider the formula,
[tex]\ln (e^m)=e^{\ln (m)}=m[/tex]
Applying the formula,
[tex]\begin{gathered} 5x=\ln (659) \\ x=\frac{1}{5}\cdot\ln (659) \\ x\approx1.30 \end{gathered}[/tex]
Thus, the solution of the given exponential equation is approximately equal to,
[tex]1.30[/tex]
