Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - 7.6 Exercises - Skill Practice - Page 520: 35

Answer

35.6

Work Step by Step

Using the rules of logarithms to solve the equation, we find: $$\log _4\left(2x\right)=\frac{40}{13} \\ \log _4\left(2x\right)=\log _4\left(64\cdot \:4^{\frac{1}{13}}\right) \\ x=32\cdot \:4^{\frac{1}{13}} \\ x=35.6$$ Checking for extraneous solutions, we see that the given solution is valid.
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