Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set - Page 861: 33



Work Step by Step

$81^{x-1}=27^{2x}$ Rewrite $81$ as $3^{4}$ and $27$ as $3^{3}$: $(3^{4})^{x-1}=(3^{3})^{2x}$ Transform this equation into $3^{4x-4}=3^{6x}$. This comes from multiplying the exponents on both sides of the equation: $3^{4x-4}=3^{6x}$ If $3^{4x-4}=3^{6x}$, then $4x-4=6x$: $4x-4=6x$ Solve for $x$: $4x-6x=4$ $-2x=4$ $x=\dfrac{4}{-2}$ $x=-2$
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