## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises - Page 456: 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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