Absolutely, let's rewrite those equations as requested.
### Part (a): Rewrite as an exponential equation
We start with the logarithmic equation:
[tex]\[ \ln x = 8 \][/tex]
To rewrite this equation in exponential form, we need to remember the fundamental relationship between logarithms and exponentials:
[tex]\[ \ln x = 8 \implies x = e^8 \][/tex]
So the exponential form of the equation is:
[tex]\[
x = e^8
\][/tex]
### Part (b): Rewrite as a logarithmic equation
We start with the exponential equation:
[tex]\[ e^4 = y \][/tex]
To rewrite this equation in logarithmic form, we use the definition of the natural logarithm, which is the inverse of the exponential function with base [tex]\(e\)[/tex]:
[tex]\[ e^4 = y \implies \ln y = 4 \][/tex]
So the logarithmic form of the equation is:
[tex]\[
\ln y = 4
\][/tex]
Therefore, the rewritten equations are:
(a) [tex]\( x = e^8 \)[/tex] \\
(b) [tex]\( \ln y = 4 \)[/tex]
