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) = 7.1\\)

Explanation:

Step1: Recall the logarithm property

The natural logarithm function \(\ln\) and the exponential function \(e^x\) are inverse functions. One of the properties of logarithms is \(\ln(e^a)=a\) for any real number \(a\).
In the given equation \(\ln(e^{x}) = 7.1\), by applying the property \(\ln(e^a)=a\), we can simplify the left - hand side.

Step2: Simplify the equation

Applying the property \(\ln(e^x)=x\) (since \(a = x\) in the property \(\ln(e^a)=a\)), the equation \(\ln(e^{x})=7.1\) simplifies to \(x = 7.1\).

Answer:

\(x = 7.1\)