SOLUTION: If log8^n= 1/2p, log2^2n=q,and q-p=4, find n.

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Question 976021: If log8^n= 1/2p, log2^2n=q,and q-p=4, find n.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%28log%28%288%5En%29%29=+1%2F2p%2C+log%28%282%5E%282n%29%29%29=q%2C+q-p=4%29, base was not indicated.

system%28n%2Alog%28%288%29%29=1%2F%282p%29%2C2n%2Alog%28%282%29%29=q%2Cq-p=4%29

system%283n%2Alog%28%282%29%29=1%2F%282p%29%2Cq=2n%2Alog%28%282%29%29%2Cq-p=4%29

system%286n%2Alog%28%282%29%29=1%2Fp%2Cq=2n%2Alog%28%282%29%29%2Cq-p=4%29

system%28p=-6n%2Alog%28%282%29%29%2Cq=2n%2Alog%28%282%29%29%2Cq-p=4%29



Substitute for p and q in the last equation, "4".

2n%2Alog%28%282%29%29%2B6n%2Alog%28%282%29%29=4

n%282%2Alog%28%282%29%29%2B6%2Alog%28%282%29%29%29=4

n%288%2Alog%28%282%29%29%29=4

n%2A2%2Alog%28%282%29%29=1

highlight%28n=1%2F%282%2Alog%28%282%29%29%29%29