Solve`(log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54`.

Answer

` x = 1/sqrt5, 25`

Explanation

`(log_(3)x)(log_(5)9)-log_(x) 25+log_(3)2=log_(3) 54`
` or (logx)/(log 3) xx(log 9)/(log 5) - 2 log_(x) 5 +log_(3)2 =3+ log_(3)2`
` or 2 log _(5) x - 2log_(x) 5 +log_(3) 2 = 3 + log_(3) 2`
` or 2 t^(2) - 2 = 3t" "("putting "log_(5) x =t)`
` or 2t^(2) - 3t - 2 = 0`
` or (2t+1)(t-2) =0`
` rArr t =- 1//2 or t = 2`
` rArr log_(5)x =- 1//2 or log_(5) x = 2`
` rArr x = 1//sqrt5, x = 25`