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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 104. (page 299)

Solve the equation.
$\log_{5} (x^{2} + x + 4) = 2$

Short Answer

Expert verified

The solution to the equation, $\log_{5} (x^{2} + x + 4) = 2$ is, $x = \frac{- 1 + \sqrt{85}}{2}$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $\log_{5} (x^{2} + x + 4) = 2$ .

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 $\log_{5} (x^{2} + x + 4) = 2$ .

Use rule of change from logarithm to exponents:

$\log_{5} (x^{2} + x + 4) = 2 x^{2} + x + 4 = 5^{2} x^{2} + x + 4 = 25 x^{2} + x - 21 = 0 x = \frac{- 1 卤 \sqrt{1 + 84}}{2} x = \frac{- 1 卤 \sqrt{85}}{2}$

The solution to the given equationis, $x = \frac{- 1 + \sqrt{85}}{2}$ .

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and verify your results using a graphing utility

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