53, Solution set of `log_x 2.log_(2x)2=log_(4x) 2` is

Options

A. `{2^(-sqrt(2)), 2^(sqrt(2))}`
B. `{(1)/(2), 2}`
C. `{(1)/(4), 4}`
D. None of these

Answer

A

Explanation

The solution set of ………………….
We have `(1)/(log_(2)x) (1)/(log_(2)2x) = (1)/(log_(2)4x), x != 1, x gt 0`
`implies (1)/(log_(2)x) (1)/(1+log_(2)x)= (1)/(2+log_(2)x)`
`implies 2+log_(2)x = log_(2)x(1+log_(2)x)`
`implies 2= (log_(2)x)^(2) implies log_(2)x = +- sqrt(2) implies x = 2^(sqrt(2)) , 2^(-sqrt(2))`