SOLUTION: given that log8^(p+2) +log8^q=r-1/3and log2^(p-2)-log2^q=2r+1 then show that p�=4+32^r

Question 1122163: given that log8^(p+2) +log8^q=r-1/3and log2^(p-2)-log2^q=2r+1 then show that p�=4+32^r
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The "^" symbol is used to represent exponents -- not to indicate the base of a logarithm. Your question is

Given that and then show that

It looks ugly (especially the way you showed it!), but everything falls in place nicely using basic rules of logarithms. Specifically, we need to use

log(a)+log(b) = log(ab)
log(a)-log(b) = log(a/b)
log base 2 of x = 3*log base 8 of x, since 8 = 2^3

(1) Given

(2) Given

(3) from (1)

(4) from (3)

(5) from (2)

(6) from (4) and (5)

(7) (definition of log base 2)
(8)
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