Accuplacer Advanced Algebra and Functions Practice Exam 2026 - Free Advanced Algebra Practice Questions and Study Guide

To solve the equation \(2e^x = 10\), the first step is to isolate the exponential term. We can start by dividing both sides of the equation by 2:

\[

e^x = \frac{10}{2} = 5.

\]

Now that we have \(e^x = 5\), we can eliminate the exponential by taking the natural logarithm of both sides. The natural logarithm, \(\ln\), is the inverse function of the exponential function \(e^x\). Thus, we apply the logarithm:

\[

\ln(e^x) = \ln(5).

\]

By the properties of logarithms, specifically that \(\ln(e^x) = x\), we can simplify the left side:

\[

x = \ln(5).

\]

Therefore, the value of \(x\) that satisfies the original equation \(2e^x = 10\) is \(\ln(5)\). This solution correctly finds \(x\) while ensuring that all necessary steps highlight the relationship between exponential and logarithmic functions.