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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 89. (page 299)

Solve the equation.
$\log_{2} (2 x + 1) = 3$

Short Answer

Expert verified

The solution to the equation, $\log_{2} (2 x + 1) = 3$ is, $x = 3.5$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $\log_{2} (2 x + 1) = 3$ .

02

Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y 鈬� a^{y} = b$

03

Step 3. Finding Solution

The given equation is $\log_{2} (2 x + 1) = 3$ .

Use rule of change from logarithm to exponents:

$\log_{2} (2 x + 1) = 3 2 x + 1 = 2^{3} 2 x = 8 - 1 x = \frac{7}{2} x = 3.5$

The solution to the given equationis, $x = 3.5$ .

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