The equation `(log)_(x^2)\ 16` + `(log)_(2x)64=3\ h a s` one irrational solution (b) no prime solution two real solutions (d) no integral solution

Options

A. one irrational solution
B. no prime solution
C. two real solutions
D. no integral solution

Explanation

`L.H.S. =(1)/(log_(2^(4))x^(2))+(1)/(log_(2^(6))2x)=3implies(1)/(1//2log_(2)x)+(1)/(1//6(1+log_(2)x))=3"let"log_(2)x=y`
`implies2/y+(6)/(1+y)=3implies2(1+y)+6y=3y(1+y)implies(y-2)(3y+1)=0impliesy=2ory=-1//3`
`log_(2)x=2impliesx=4andlog_(2)x=(-1)/(3)impliesx=2^(-1//3)"]"`