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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.78 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{9} x + 3 \log_{3} x = 14$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 81$

Step by step solution

01

Given information

We are given an equation $\log_{9} x + 3 \log_{3} x = 14$

02

Change the base

We get,

$\log_{9} x + 3 \log_{3} x = 14 \frac{\log_{3} (x)}{\log_{3} 9} + 3 \log_{3} x = 14 \frac{\log_{3} (x)}{2} + 3 \log_{3} x = 14 \log_{3} (x) + 6 \log_{3} x = 28 7 \log_{3} x = 28 \log_{3} x = 4$

03

use the formula y=logax⇔x=ay

We get,

$\log_{3} (x) = 4 x = 3^{4} x = 81$

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