Question

Please help me answer this..

Suppose that

2^(x/2)= p

3^(x/3-1)= q

[5^(x/2)]/3 = r

Express (0.48)^x in terms of p, q and/ or r.


this question came from our reviewer.. please and thank you!

Answer 1

.48 = 48/100 = 12/25 = 2*2*3/(5*5)


if 2^(x/2)= p then 2 = p^(2/x)
if 3^(x/3-1)= q or 3^(x-3)/3) then 3 = q^(3/(x-3))
if [5^(x/2)]/3 = r then 5 = (3r)^(2/x)
so .48 = 2*2*3/(5*5)
= (p^(2/x))(p^(2/x)(q^(3/(x-3)))/[(3r)^(2/x)*(3r)^(2/x)]

= 2^x * 3^(3/(x-3)) / (3r)^x

Answer 2

forgot to finish it, since it was .48^x

so my answer 2^x * 3^(3/(x-3)) / (3r)^x raised to the x
or [2^x * 3^(3/(x-3)) / (3r)^x]^x