College Algebra (10th Edition)

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

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding: 100

Answer

$x=\frac{-1}{5}$

Work Step by Step

RECALL: $\log_a{x}=y \longrightarrow a^y = x$ Use the rule above to obtain: $\log_6{36}=5x +3 \\\longrightarrow 6^{5x+3}=36$ Note that $36=6^2$. Thus, the expression above is equivalent to: $6^{5x+3}=6^2$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $5x+3=2$ Subtract by 3 on both sides of the equation to obtain: $5x=2-3 \\5x=-1$ Divide by 5 on both sides of the equation to obtain: $x=\frac{-1}{5}$
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