Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 352: 27

a.) 2 b.) 2 c.) 10

$Evaluate$ $the$ $expression:$ a.) $\log_6 36$ b.) $\log_9 81$ c.) $\log_7 7^{10}$ a.) $\log_6 36$ Rewrite 36 as $6^2$ [Note: $6^2 = 6\times6 = 36$] $\log_6 6^2$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_6 6^2 = 2$ b.) $\log_9 81$ Rewrite 81 as $9^2$ [Note: $9^2 = 9\times9 = 81$] $\log_9 9^2$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_9 9^2 = 2$ c.) $\log_7 7^{10}$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_7 7^{10} = 10$