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: 48


$$x=\frac{5\ln \left(6\right)+4\ln \left(3\right)}{\ln \left(12\right)}$$

Work Step by Step

Using the rules of logarithms and exponents, we find: $$\ln \left(3^{x+4}\right)=\ln \left(6^{2x-5}\right)\\ \left(x+4\right)\ln \left(3\right)=\left(2x-5\right)\ln \left(6\right) \\ x=\frac{5\ln \left(6\right)+4\ln \left(3\right)}{\ln \left(12\right)} $$
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