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: 99

Answer

$x=2$

Work Step by Step

RECALL: $\log_a{x}=y \longrightarrow a^y = x$ Use the rule above to obtain: $\log_3{243}=2x +1 \\\longrightarrow 3^{2x+1}=243$ Note that $243=3^5$. Thus, the expression above is equivalent to: $3^{2x+1}=3^5$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $2x+1=5$ Subtract 1 on both sides of the equation to obtain: $2x=4$ Divide by 2 on both sides of the equation to obtain: $x=2$
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