College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 72

Answer

$x=\frac{1}{2}$

Work Step by Step

We rewrite the 8 on the right side, so that the base is $2$ on both sides. $2^{6-3x}=8^{x+1}$ $2^{6-3x}=(2^3)^{x+1}$ By the law of exponents: $(a^x)^y=a^{xy}$ $(2^3)^{x+1}=2^{3x+3}$ Thus, the given equation is equivalent to: $2^{6-3x} = 2^{3x+3}$ Then we set the exponents equal, because the two sides are equal only if the powers are equal too: if $b^m=b^n$ and $b \ne0$ , $b \ne1$ then $m=n$ $6-3x=3x+3 6-3=3x+x$ $3=6x$ $\frac{3}{6}=\frac{6x}{6} \\\frac{1}{2}=x$
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