Question

instructions: eval
3.
a) $log_{6}36 = $
b) $log_{2}32 = $
c) $log_{4}64 = $
d) $log_{3}81 = $

Explanation:

Step1: Rewrite 36 as $6^2$

$\log_{6}36 = \log_{6}6^2$

Step2: Apply log power rule: $\log_b b^x=x$

$\log_{6}6^2 = 2$

Step3: Rewrite 32 as $2^5$

$\log_{2}32 = \log_{2}2^5$

Step4: Apply log power rule

$\log_{2}2^5 = 5$

Step5: Rewrite 64 as $4^3$

$\log_{4}64 = \log_{4}4^3$

Step6: Apply log power rule

$\log_{4}4^3 = 3$

Step7: Rewrite 81 as $3^4$

$\log_{3}81 = \log_{3}3^4$

Step8: Apply log power rule

$\log_{3}3^4 = 4$

Answer:

A) $2$
B) $5$
C) $3$
D) $4$