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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. 10.50 (page 1031)

Solve:
$a) \log_{3} (4 x + 3) = 3 b) \ln (e^{4 x}) = 4$

Short Answer

Expert verified

Part (a) The value of $x$ is $6$ .

Part (b) The value of $x$ is $1$ .

Step by step solution

01

Step 1. Given information.

The given expressions are,

$a) \log_{3} (4 x + 3) = 3 b) \ln (e^{4 x}) = 4$

02

Step 2. Solving part (a).

Now, we will convert the given expression to exponential form and simplify.

$\log_{3} (4 x + 3) = 3 4 x + 3 = 3^{3} 4 x + 3 = 27 4 x = 24 x = 6$

Checking the result.

$\log_{3} (4 (6) + 3) = 3 4 (6) + 3 = 3^{3} 24 + 3 = 27 27 = 27$

Therefore, this is true.

03

Step 3. Solving part (b).

Now, we will convert the given expression to exponential form and simplify.

$\ln (e^{4 x}) = 4 e^{4} = e^{4 x} 4 x = 4 x = 1$

Checking the result.

$\ln (e^{4 (1)}) = 4 e^{4} = e^{4}$

Therefore, this is true.

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