Question

solve the following logarithmic equation, using a calculator if necessary to evaluate the logarithm. write your answer as a fraction or round your answer to one decimal place. \\(\ln(e^{x}) = 23.1\\) answer how to enter your answer (opens in new window)

Explanation:

Step1: Recall logarithm property

The natural logarithm \(\ln(x)\) and the exponential function \(e^x\) are inverse functions, so \(\ln(e^a)=a\) for any real number \(a\).
Applying this property to the left - hand side of the equation \(\ln(e^{x}) = 23.1\), we get:
Since \(\ln(e^{x})\) simplifies to \(x\) (by the inverse property of logarithms and exponentials, \(\ln(e^{y})=y\) where \(y = x\) in our case), the equation \(\ln(e^{x})=23.1\) becomes \(x=23.1\).

Answer:

\(23.1\)