Question

write the following logarithmic equation as an exponential equation. do not simplify your answer.
ln8 = 5x

Explanation:

Step1: Recall the definition of natural logarithm

The natural logarithm \(\ln a\) is defined as \(\log_{e} a\), where \(e\) is the base of the natural logarithm. So, \(\ln 8=\log_{e}8\).

Step2: Use the logarithmic to exponential conversion formula

The logarithmic equation \(\log_{b}y = x\) can be converted to the exponential equation \(b^{x}=y\). Here, \(b = e\), \(y = 8\), and \(x = 5x\) (from the equation \(\log_{e}8=5x\)).
Applying the conversion formula, we get \(e^{5x}=8\).

Answer:

\(e^{5x}=8\)