Answer
a.) 5
b.) 17
c.) 0
Work Step by Step
$Evaluate$ $the$ $expression:$
a.) $\log_2 32$
b.) $\log_8 8^{17}$
c.) $\log_6 1$
a.) $\log_2 32$
Rewrite 32 as $2^5$ [Note: $2^5 = 2\times2\times2\times2\times2 = 32$]
$\log_2 2^5$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_2 2^5 = 5$
b.) $\log_8 8^{17}$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_8 8^{17} = 17$
c.) $\log_6 1$
Rewrite 1 as $6^0$ [Note: Any number or variable to the power of 0 equals 1]
$\log_6 6^0$
Use the Third Property of Logarithms: $\log_a a^x = x$
$\log_6 6^0 = 0$