Question

if 3^p = 5^q = 45^r , then find the relation between p, q and r

Answer 1

hey buddy here is your answer
Let 3^p=5^q=45^r=k
then,
3^p=k
3=k^1/p...............(i)
5^q=k
5=k^1/q.............(ii)
45^r=k
45=k^1/r............(iii)
now comparing (i) (ii) and (iii)

3^2×5=45
replacing 3,5,45 by their values
(k^1/p)^2 × k^1/q=k^1/r
k^2/p × k^1/q=k^1/r
k^2/p+1/q=k^1/r
the base is same to both side
thus now,
2/p+1/q=1/r...............[this is the relation between p,q and r.]






HOPE YOU UNDERSTAND