Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set: 13

Answer

$x=\dfrac{4}{3}+\dfrac{\log11}{3\log7}\approx1.7441$

Work Step by Step

$7^{3x-4}=11$ Apply $\log$ to both sides of the equation: $\log7^{3x-4}=\log11$ Take $3x-4$ down to multiply in front of its respective $\log$: $(3x-4)\log7=\log11$ Solve for $x$: $3x-4=\dfrac{\log11}{\log7}$ $3x=4+\dfrac{\log11}{\log7}$ $x=\dfrac{4+\dfrac{\log11}{\log7}}{3}$ $x=\dfrac{4}{3}+\dfrac{\log11}{3\log7}\approx1.7441$
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