SOLUTION: If logk = c logv + logp , what does k equal?

Algebra ->  Sequences-and-series -> SOLUTION: If logk = c logv + logp , what does k equal?       Log On


   



Question 1033283: If logk = c logv + logp , what does k equal?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if log(x) = log(y), then x = y.

that's the concept involved here.

also, a*log(b) = log(b^a)

also, log(x) + log(y) = log(x*y)

all these concepts come into play.

start with:

log(k) = c*log(v) + log(p)

the order you do these things is important.

since c*log(v) is equal to log(v^c), your equation becomes log(k) = log(v^c) + log(p)

since log(v^c) + log(p) becomes log(v^c*p), your equation becomes log(k) = log(v^c*p)

since log(k) = log(v^c*p), then k must be equal to v^c*p

that's your solution.

k = v^c*p


for example, if you let p = 3, v = 2, c = 5, then v^c*p = 96.

k would have to be equal to 96,

you would then get log(96) = log(96).