Question

b) $3^4 = 81$
$circ$ $log_{3}(81) = 4$
$circ$ $log_{4}(81) = 3$
$circ$ $log_{3}(4) = 81$
$circ$ none of the above

c) $5^4 = 625$
$circ$ $log_{5}(625) = 4$
$circ$ $log_{4}(625) = 5$
$circ$ $log_{5}(4) = 625$
$circ$ none of the above

Explanation:

Step1: Recall log-exponential conversion rule

For $b^x = y$, $\log_b(y) = x$

Step2: Apply rule to part b)

Given $3^4 = 81$, base $b=3$, $x=4$, $y=81$. So $\log_3(81)=4$

Step3: Apply rule to part c)

Given $5^4 = 625$, base $b=5$, $x=4$, $y=625$. So $\log_5(625)=4$

Answer:

b) $\log_3(81) = 4$
c) $\log_5(625) = 4$