College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check - Page 425: 57


$x = 5$

Work Step by Step

To solve the given exponential equation, make the two sides have the same base. Then, equate the exponents and solve for the unknown variable. Since $27=3^3$, the given equation is equivalent to: $3^{2x-7} = 3^3$ Use the rule $a^m = a^n \longrightarrow m=n$ to obtain: $2x-7 = 3$ Add $7$ to both sides to obtain: $2x = 10$ Divide $2$ to both sides to obtain: $x = 5$
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