Answer
a.) 7
b.) 3
c.) 3
Work Step by Step
$Evaluate$ $the$ $expression:$
a.) $\log_3 3^7$
b.) $\log_4 64$
c.) $\log_5 125$
a.) $\log_3 3^7$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_3 3^7 = 7$
b.) $\log_4 64$
Rewrite 64 as $4^3$ [Note: $4^3 = 4\times4\times4 = 64$]
$\log_4 4^3$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_4 4^3 = 3$
c.) $\log_5 125$
Rewrite 125 as $5^3$ [Note: $5^3 = 5\times5\times5 = 125$]
$\log_5 5^3$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_5 5^3 = 3$
