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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 109. (page 299)

Solve the equation.
$2 路 10^{2 - x} = 5$

Short Answer

Expert verified

The solution to the equation, $2 路 10^{2 - x} = 5$ is, $x = 2 - \log \frac{5}{2}$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $2 路 10^{2 - x} = 5$ .

02

Step 2. Formula used

Common Logarithm:
$\log 10 = 1$

03

Step 3. Finding Solution

The given equation is $2 路 10^{2 - x} = 5$ .

Divide both sides by $2$ .

$\frac{2 路 10^{2 - x}}{2} = \frac{5}{2}$

$10^{2 - x} = \frac{5}{2}$

Take logarithm on both sides.

$\log 10^{2 - x} = \log \frac{5}{2} (2 - x) \log 10 = \log \frac{5}{2} 2 - x = \log \frac{5}{2} x = 2 - \log \frac{5}{2}$

The solution to the given equationis, $x = 2 - \log \frac{5}{2}$ .

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