Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 39


$x=0$ $x=0.861$

Work Step by Step

$4^x=5^{x^2}$ $\log_44^x=\log_45^{x^2}$ $x=x^2\log_45$ $-x^2\log_45+x=0$ $-x(x\log_45-1)=0$ $-x=0$ $x=0$ $x\log_45-1=0$ $x\log_45=1$ $x=\frac{1}{\log_45}=\frac{1}{\frac{\ln5}{\ln4}}=\frac{\ln4}{\ln5}=0.861$
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