Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1-6 - Cumulative Review: 8

Answer

$x = \frac{\frac{\ln 45}{\ln 2} + 7}{3} \approx 4.164$

Work Step by Step

$2^{3x-7} = 45$ $3x - 7 = \ln_2 45$ $3x = \log_2 45 + 7$ $x = \frac{\log_2 45 + 7}{3}$ $x = \frac{\frac{\ln 45}{\ln 2} + 7}{3}$ $x \approx 4.164$ Check: $2^{3(\frac{\frac{\ln 45}{\ln 2} + 7}{3})-7} \overset{?}{=} 45$ $2^{\frac{\ln 45}{\ln 2} + 7-7} \overset{?}{=} 45$ $2^{\frac{\ln 45}{\ln 2} } \overset{?}{=} 45$ $45 = 45$
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