Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 82

Answer

$x = 5$

Work Step by Step

RECALL: $a \cdot \log_b{x} = \log_b{(x^a)}$ Use the rule above to obtain: $\log{(x^3)}=\log{125}$ Use the rule "$\log_b{a} =\log_b{c} \longrightarrow a = c$" to obtain: $x^3=125 \\x^3=5^3$ Take the cube root of both sides to obtain: $x=\sqrt[3]{5^3} \\x = 5$
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