Question:
[tex]e^{-5x}=7.4[/tex]
Step 1: Apply the exponent rule but taking ln of both sides
[tex]\begin{gathered} e^{-5x}=7.4 \\ -5x=\ln 7.4 \end{gathered}[/tex]
Step 2:Divide both sides by -5
[tex]\begin{gathered} -5x=\ln 7.4 \\ \frac{-5x}{-5}=\frac{\ln 7.4}{-5} \\ x=\frac{\ln7.4}{-5} \end{gathered}[/tex]
Hence,
The value of x is
[tex]\begin{gathered} x=\frac{\ln7.4}{-5} \\ x=-4.003 \end{gathered}[/tex]
Hence,
The final answer is = -0.4003
