Sure! Let's rewrite the given exponential equation as a logarithmic equation step by step.
Step 1: Start with the given equation.
[tex]\[ 4 e^x = 16 \][/tex]
Step 2: Divide both sides of the equation by 4 to isolate [tex]\( e^x \)[/tex].
[tex]\[ e^x = \frac{16}{4} \][/tex]
Step 3: Simplify the fraction on the right-hand side.
[tex]\[ e^x = 4 \][/tex]
Step 4: To solve for [tex]\( x \)[/tex], take the natural logarithm (ln) of both sides of the equation.
[tex]\[ \ln(e^x) = \ln(4) \][/tex]
Step 5: Use the logarithmic property [tex]\( \ln(e^x) = x \cdot \ln(e) \)[/tex]. Since [tex]\( \ln(e) = 1 \)[/tex], this simplifies to:
[tex]\[ x = \ln(4) \][/tex]
Thus, the logarithmic form of the given exponential equation is:
[tex]\[ x = \ln(4) \][/tex]
