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Ive the following equation. Write the answer in terms of the natural logarithm. \( e^{3 x}=6 \) The solution set is \( \{ \). (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.

Ask by Kirk Carlson. in the United States
Mar 18,2025

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\( x = \frac{\ln(6)}{3} \)

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To solve the equation \( e^{3x} = 6 \), you can take the natural logarithm of both sides. Doing that gives you: \[ 3x = \ln(6) \] Next, divide both sides by 3 to isolate \( x \): \[ x = \frac{\ln(6)}{3} \] So, the solution set is \( \left\{ \frac{\ln(6)}{3} \right\} \).

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