Let's rewrite it the first one
[tex]e^y=2[/tex]
[tex]\begin{gathered} \log _ee^y=\log _e2 \\ y=\log _e2 \end{gathered}[/tex]
When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.
Rewriting the second one:
[tex]\begin{gathered} \ln (x)=9 \\ \log _ex=9 \\ x=e^9 \end{gathered}[/tex]
Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9
