Given the following 2^p=3^q=12^r,

Find r in terms of p and q. Please help, thanks!

Answer:(pq)/ (p+2q)

from above

2 = 12^(r/p)
3 = 12^(r/q)

now

12 = 2 ^2 * 3 = 12^(^2r/p) 12^(r/q)

or 1 = 2r/p + \r/q

or 1/r = (2/p+ 1/q) = (p+2q) / (pq) or r = pq/(p + 2q)