Problem 26 - College Algebra Essentials

Question

Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{x}=0.83$$

Step-by-Step Solution

Answer

The solution to the equation \(e^{x} = 0.83\) is \(x = \ln(0.83)\), which is approximately -0.19 after rounding to two decimal places.

Step 1: Rewrite in logarithmic form

To start solving the problem, we first change the equation from exponential form to logarithmic form. Using the definition of a logarithm, we can write this as \(x = \ln(0.83)\).

Step 2: Use a calculator to find decimal solution

In the second step, use a calculator to find the decimal equivalent of \(x\), rounded to two decimal places.