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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 108. (page 299)

Solve the equation.
$8 路 10^{2 x - 7} = 3$

Short Answer

Expert verified

The solution to the equation, $8 路 10^{2 x - 7} = 3$ is, $x = \frac{1}{2} (\log \frac{3}{8} + 7)$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $8 路 10^{2 x - 7} = 3$ .

02

Step 2. Formula used

Common logarithm:

$\log 10 = 1$

03

Step 3. Finding Solution

The given equation is $8 路 10^{2 x - 7} = 3$

Divide both sides by $8$ .

$\frac{8 路 10^{2 x - 7}}{8} = \frac{3}{8} 10^{2 x - 7} = \frac{3}{8}$

Take logarithm on both sides.
$\log 10^{2 x - 7} = \log \frac{3}{8} (2 x - 7) \log 10 = \log \frac{3}{8} 2 x - 7 = \log \frac{3}{8} 2 x = \log \frac{3}{8} + 7 x = \frac{1}{2} (\log \frac{3}{8} + 7)$

The solution to the given equationis, $x = \frac{1}{2} (\log \frac{3}{8} + 7)$ .

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