Hello!
We have the expression:
[tex]e^x=7.1[/tex]
The first step is to write the number as a fraction, look:
[tex]e^x=\frac{71}{10}[/tex]
Now, let's calculate the natural logarithm on both sides of the equation:
[tex]\ln(e^x)=\ln\left(\right.\frac{71}{70})[/tex]
We can simplify it as:
[tex]\begin{gathered} \cancel{\mathrm{ln}}(\cancel{e}^x)=\operatorname{\ln}(\frac{71}{70}) \\ \\ x=\mathrm{ln}(\frac{71}{70}) \end{gathered}[/tex]
Now, let's calculate it:
[tex]\begin{gathered} x=\ln(\frac{71}{70}) \\ \\ x\cong1.96 \end{gathered}[/tex]
Answer:
Alternative D. x = 1.96.
