Question

question 4 of 10 what is the solution to the equation below? round your answer to two decimal places. \\( \ln x = 2.1 \\) a. \\( x = 8.17 \\) b. \\( x = 0.74 \\) c. \\( x = 5.71 \\) d. \\( x = 7.51 \\)

Explanation:

Step1: Recall the inverse of natural log

The natural logarithm $\ln x$ is the inverse of the exponential function with base $e$, so if $\ln x = a$, then $x = e^a$.

Step2: Apply the inverse to the equation

Given $\ln x = 2.1$, we rewrite it as $x = e^{2.1}$.

Step3: Calculate $e^{2.1}$

Using a calculator, $e^{2.1}\approx 8.1661699$.

Step4: Round to two decimal places

Rounding $8.1661699$ to two decimal places gives $8.17$.

Answer:

A. $x = 8.17$