Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 296: 98



Work Step by Step

We know that by definition then $log_a {y}=x$, then $y=a^x$. Hence if $log_3 {(243)}=2x+1$, then $3^{2x+1}=343=3^5$. The base is the same on the two sides of the equation, hence the exponents must be equal. Solve the equation above to obtain: \begin{align*}5=2x+1\end{align*} \begin{align*}4=2x\end{align*} \begin{align*}x=2\end{align*}
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