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: 27

Answer

$\log_3{9}=2$

Work Step by Step

Let $x=\log_3{9}.$ RECALL: $\log_{a}{y} = b \longleftrightarrow a^b = y.$ Use the definition above to convert the equation to an exponential equation and have $3^x=9.$ Write each side in base 3 to have $3^x=3^2.$ The bases are the same, so the exponents must be equal. Thus, $x=2.$ Therefore $\log_3{9}=2$.
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