8=4^3/2 in log form is? (10 pts)?

8 = 4^(3/2)

log(base4) 8 = 3/2

Simply take the base number on the right side to be the base of log on the left side:
8 = 4^(3/2)
log₄ 8 = 3/2

Done

8=4^3/2
take logs of both sides:log 8=log4^3/2
using rule of logs:log 8=3/2log4
using another rule of logs:3/2- log (8/4)
so i think it is 3/2 -log 2

The usual (in base 10 or any other base)
log 8 = 3/2 log 4. Since log 4 is about 0.6 and log 8 is about 0.9, this seems pretty easy to verify.

Let log be log to base 4

8 = 4^(3/2)

log 8 = 3/2 log 4

log 8 = 3/2

b^y = x → y = log_b(x)

8 = 4^(3/2)
3/2 = log_4(8)

log (base 4) 8 = 3/2 is the log form.

4^(3/2) = (64)^(1/2) = 8

log form is in the form a=log (baseb) c

which means a is the exponent that makes b = to c

3/2 = log(base4) 8