Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - Guided Practice for Example 1 - Page 515: 1



Work Step by Step

In order to solve a problem like this where the variable is in the exponent on both sides of the equation, we try to get the same base on both sides of the equation. After we do this, we set the numbers in the exponent equal to each other to find: $$\left(3^2\right)^{2x}=27^{x-1} \\ 3^{2\cdot \:2x}=3^{3\left(x-1\right)} \\ 4x=3\left(x-1\right) \\ x=-3$$
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