Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises: 26

Answer

The given logarithm is undefined.

Work Step by Step

Let $x=\log_5{-25}.$ RECALL: $\log_{a}{y} = b \longleftrightarrow a^b = y.$ Use the definition above to convert the equation to an exponential equation and have $5^x=-25.$ Note $5$ is raised to any power, the result will never be negative. Thus, the given equation has no solution. This means that the given logarithmic expression is undefined.
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