it might help to write everything in terms of powers of sqrt(2)
64=2^6=sqrt(2)^12
32768=2^15=sqrt(2)^30
So, if u=sqrt(2), we have
5u^(3x) * u^(12(2x+2)) = u^30x
5u^(3x) * u^(24x+24) = u^30x
You sure that 5 belongs there, or is this just problem 5?
Without the 5, x=8 since we then just have to add the powers to get
3x+24x+24=30x
x=8
With the 5, things get messier.
Solve?
5 sqrt 2^3x * 64^2x+2 =32768^x
2 answers
Yeah I'm sure 5 is there because it's power cube of 5sqrt