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 - 7.6 Exercises - Skill Practice - Page 520: 53



Work Step by Step

Given: $5^{2x}+20.5^x-125=0\\(5^x+25)(5^x-5)=0$ We have $5^x+25=0\\5^x=-25$ This gives no real solution. and $5^x-5=0\\5^x=5\\x=1$ Check: $5^{2(1)}+20.5^1-125=0\\0=0$ Hence, the only real solution is $x=1$
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