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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.77 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{16} x + \log_{4} x + \log_{2} x = 7$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 16$

Step by step solution

01

Given information

We are given an equation $\log_{16} x + \log_{4} x + \log_{2} x = 7$

02

Change the base

We get,

$\log_{16} x + \log_{4} x + \log_{2} x = 7 \frac{\log_{2} (x)}{\log_{2} (16)} + \frac{\log_{2} (x)}{\log_{2} (4)} + \log_{2} (x) = 7 \frac{\log_{2} (x)}{\log_{2} {(2)}^{4}} + \frac{\log_{2} (x)}{\log_{2} (2^{2})} + \log_{2} (x) = 7 \frac{\log_{2} (x)}{4} + \frac{\log_{2} (x)}{2} + \log_{2} (x) = 7 \log_{2} (x) + 2 \log_{2} (x) + 4 \log_{2} (x) = 28 7 \log_{2} (x) = 28 \log_{2} (x) = 4$

03

Solve the equation

We get,

$\log_{2} (x) = 4 U s e : y = \log_{a} (x) 鈬� x = a^{y} x = 2^{4} x = 16$

04

Conclusion

The value of x satisfying the equation $x = 16$ .

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Most popular questions from this chapter

Solve the equation. Verify your results using a graphing utility.

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