Exponential and Logarithmic Functions Converting between natural logarithmic and exponential equi
Rewrite each equation as requested.
(a) Rewrite as an exponential equation.
\[
\ln 8=y
\]
(b) Rewrite as a logarithmic equation.
\[
e^{9}=x
\]
Answer
Rewrite the equation \(e^{9}=x\) as a logarithmic equation. The logarithm is the inverse of the exponential function, so the equation can be rewritten as \(\ln x=9\).
Step 1 ：Rewrite the equation \(\ln 8=y\) as an exponential equation. The natural logarithm is the inverse of the exponential function, so the equation can be rewritten as \(e^{y}=8\).
Step 2 ：Rewrite the equation \(e^{9}=x\) as a logarithmic equation. The logarithm is the inverse of the exponential function, so the equation can be rewritten as \(\ln x=9\).
