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: 33

Answer

$x=-2$

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 $x$: $4x-6x=4$ $-2x=4$ $x=\dfrac{4}{-2}$ $x=-2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.