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: 31

Answer

$\log_5{125}=3$

Work Step by Step

Let $x=\log_5{125}.$ RECALL: $\log_{a}{y} = b \longleftrightarrow a^b = y.$ Use the definition above to convert the equation to an exponential equation and have $5^x=125.$ Write each side in base 5 to have $5^x=5^3.$ The bases are the same, so the exponents must be equal. Thus, $x=3.$ Therefore $\log_5{125}=3$.
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