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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 332 (page 1055)

In the following exercises, solve each equation.
$\ln (e^{5 x}) = 30$ .

Short Answer

Expert verified

The solution is $x = 6$ .

Step by step solution

01

Step 1 Given equation is,

$\ln (e^{5 x}) = 30$ .

The objective is, we need to find the solution for the given equation.

We know that, $\ln (e^{x}) = x$ .

02

Step 2 Apply the property in the given equation.

$5 x = 30 x = \frac{30}{5} x = 6$

03

Step 3 Let us check the answer.

Substitute $x = 6$ in the given equation.

$\ln (e^{5 (6)}) = 30 \ln (e^{30}) = 30 30 = 30$

which is true.

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Most popular questions from this chapter

In the following exercises, match the graphs to one of the following functions:

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