Chapter 10: Q. 202 (page 1035)

In the following exercises, solve each logarithmic equation.
$\ln (e^{4 x}) = 8$

Short Answer

Expert verified

The solution is $x = 2$ .

Step by step solution

Step 1. Rewrite in exponential form

Consider the logarithmic equation $\ln (e^{4 x}) = 8$ .

Its equivalent exponential form is given as

$e^{8} = e^{4 x}$

Step 2. Equate the exponents and solve for x

In the equation $e^{8} = e^{4 x}$ , since the bases are the same the exponents are equal.

$8 = 4 x$

Divide both sides by $4$ .

$\begin{array}{rcl} \frac{8}{4} & = & \frac{4 x}{4} \\ 2 & = & x \end{array}$

Step 3. Check the solution

Substitute $2$ for $x$ in the original equation, we get

$\begin{array}{rcl} \ln (e^{4 x}) & = & 8 \\ \ln (e^{4 \times 2}) & = & 8 \\ \ln (e^{8}) & = & 8 \\ e^{8} & = & e^{8} \end{array}$

So we get a true statement, thus the found solution is correct.

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In the following exercises, solve each logarithmic equation.
$\ln (e^{4 x}) = 8$

Short Answer

Step by step solution

Step 1. Rewrite in exponential form

Step 2. Equate the exponents and solve for x

Step 3. Check the solution

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In the following exercises, solve each logarithmic equation. lne4x=8

Short Answer

Step by step solution

Step 1. Rewrite in exponential form

Step 2. Equate the exponents and solve for x

Step 3. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each logarithmic equation.
$\ln (e^{4 x}) = 8$