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Chapter 11: Q62. (page 582)

Solve each equation.
$e^{3 x} = 4$

Short Answer

Expert verified

The solution to the equation is $\frac{1}{3} \ln (4)$ .

Step by step solution

01

Step 1. Given Information.

Given equation is $e^{3 x} = 4$

02

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l} e^{3 x} = 4 \\ \ln (e^{3 x}) = \ln (4) \\ 3 x = \ln (4) \\ x = \frac{1}{3} \ln (4) \end{array}$

03

Step 3. Conclusion.

Hence, the solution to the equation is $x = \frac{1}{3} \ln (4)$ $x = \frac{1}{3} \ln (4)$ .

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