Sure, let's rewrite the given exponential equation as a logarithmic equation.
We start with the given exponential equation:
[tex]\[ 4 e^x = 16 \][/tex]
1. Isolate the Exponential Term:
First, we need to isolate the exponential term [tex]\( e^x \)[/tex] by dividing both sides of the equation by 4:
[tex]\[ e^x = \frac{16}{4} \][/tex]
2. Simplify the Right-Hand Side:
Simplifying the right-hand side of the equation results in:
[tex]\[ e^x = 4 \][/tex]
3. Rewrite the Equation in Logarithmic Form:
Now, we can convert the exponential equation to its equivalent logarithmic form. The base of the exponential is [tex]\( e \)[/tex], so we use the natural logarithm (ln):
[tex]\[ x = \ln(4) \][/tex]
Thus, the exponential equation [tex]\( 4 e^x = 16 \)[/tex] can be rewritten as the logarithmic equation:
[tex]\[ x = \ln(4) \][/tex]
This is the required logarithmic form of the given exponential equation.
