Problem

Solve the exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. \[ e^{x}=20.96 \] The solution set expressed in terms of logarithms is $\{\square\}$. (Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the

Solution

Step 1 :Solve the exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.

Step 2 :The equation is \(e^{x}=20.96\).

Step 3 :To solve for \(x\), we take the natural logarithm of both sides of the equation.

Step 4 :This gives us \(x = \ln(20.96)\).

Step 5 :Using a calculator, we find that \(x \approx 3.0426158594528414\).

Step 6 :\(\boxed{x \approx 3.0426158594528414}\) is the solution to the equation.

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Source: https://solvelyapp.com/problems/A6Na2zDPHI/

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