log base b 64 - log base b 16 = log base 4 16

Question

solve for the variable..

i got to the part as far as:

(log 4/log b) = 2

now i m stuck at how i can isolate the b. plz help!

Answer 1

look at your right side
isn't log₄ 16 = 2 ???

so you have:
log_b 64 - log_b16 = 2
log_b(64/16) = 2
log_b 4 = 2
or
b^2 = 4
b = 2

from your:

log4/logb = 2
cross-multiply
log4 = 2logb
log4 = log b^2
then 4 = b^2
b = 2 , just like above

Answer 2

log b (4) = 2

b^log b( 4) = 4

so b^logb(4) = b^2
so
b^2 = 4

b = 2

Answer 3

Ohh alright! Thank you :)