`6(log_x2 - log_4x)+7 = 0`
`=>6(log_2 2/(log_2 x) - log_2x/log_2 4) +7 = 0`
`=>6(1/(log_2 x) - log_2x/2) +7 = 0`
Let `log_2x =t`, then our equation becomes,
`=>6(1/t - t/2)+7 =0`
`=>12-6t^2+14t = 0`
`=>3t^2- 7t -6 =0`
`=>3t^2- 9t + 2t -6 =0`
`=>(t-3)(3t+2) = 0`
`=>t = 3 or t = -2/3`
`=>log_2 x = 3 or log_2 x = -2/3`
`=>x = 2^3 or x = 2^(-2/3).`
