SOLUTION: Given that 'p' equals log16 to the base 'q' (p=logq 16), express in terms of p: logq (8q) (basically log (8q) to the base 'q'. i managed to answer a previous question l

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given that 'p' equals log16 to the base 'q' (p=logq 16), express in terms of p: logq (8q) (basically log (8q) to the base 'q'. i managed to answer a previous question l      Log On


   



Question 290793: Given that 'p' equals log16 to the base 'q' (p=logq 16),
express in terms of p:
logq (8q) (basically log (8q) to the base 'q'.
i managed to answer a previous question linked to this one asking me to express log2 to the base q in terms of p and i managed to get p/4 which is correct.. so i kinda know what i'm doing so far :)
thank you for your time and help
maxine

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Given that 'p' equals log16 to the base 'q' (p=logq 16),
express in terms of p:
.
p=log%28q%2C16%29
.
q%5Ep=q%5Elog%28q%2C16%29
.
q%5Ep=16
.
q%5Ep=16
.
q=16%5E%281%2Fp%29
That is,
q equals 16 raised to the power of 1/p
or
q equals the pth root of 16.