# Chapter 5 - 5.3 - Properties of Logarithms - 5.3 Exercises - Page 385: 30

$\log_42+\log_432=3$

#### Work Step by Step

Use the Power Property. Also, remeber that $\log_aa=1$: $\log_42+\log_432=\log_4\sqrt 4+\log_4(\sqrt 4·16)=\log_44^{\frac{1}{2}}+\log_4(4^{\frac{1}{2}}·4^2)=\frac{1}{2}\log_44+\log_44^{\frac{5}{2}}=\frac{1}{2}\log_44+\frac{5}{2}\log_44=\frac{1}{2}(1)+\frac{5}{2}(1)=\frac{6}{2}=3$

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