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: 13

Answer

$x=4$

Work Step by Step

Note that: $\frac{1}{27}=\frac{1}{3^3}=3^{-3}$ Write $\frac{1}{27}$ as $3^{-3}$ to obtain: $3^{1-x}=3^{-3}$ RECALL: If $a^x = a^y$, then $x=y$. Use the rule above to obtain: $\begin{array}{cccc} \\&3^{1-x}&=&3^{-3} \\&1-x&=&-3 \\&-x&=&-3-1 \\&-x&=&-4 \\&-1(-x)&=&-4(-1) \\&x&=&4\end{array}$
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