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) = 7.3\\) answer how to enter your answer (opens in new window) 3 points \\(x = \\)

Explanation:

Step1: Recall logarithm property

The natural logarithm $\ln$ and the exponential function $e^x$ are inverse functions, so $\ln(e^a)=a$ for any real number $a$.
Here, in the equation $\ln(e^x) = 7.3$, by the inverse property of $\ln$ and $e^x$, we can simplify the left - hand side.

Step2: Simplify the equation

Applying the property $\ln(e^a)=a$ to $\ln(e^x)$, we get $x = 7.3$.

Answer:

$x = 7.3$