College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding - Page 465: 43


$x = \dfrac{\ln{10}}{\ln{2}}\approx 3.322$

Work Step by Step

Take the natural logarithm of both sides to obtain: $\ln{2^x} = \ln{10}$ Use the rule $\ln{a^x} = x \cdot \ln{a}$ to obtain: $x\cdot \ln{2} = \ln{10}$ Divide both sides of the equation by $\ln{2}$ to obtain: $\dfrac{x\cdot \ln{2}}{\ln{2}}=\dfrac{\ln{10}}{\ln{2}} \\x = \dfrac{\ln{10}}{\ln{2}} \\x \approx 3.322$
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