`log_(2)sqrt(x)+log_(2)sqrt(x)=4`

(1)/(2)log_(10)x+3log_(10)sqrt(2+x)=log_(10)sqrt(x(x+2))+2

Find the value of x satisfying the equation,sqrt((log_(3)3sqrt(3)x+log_(x)3sqrt(3)x)*log_(3)x^(3))+sqrt(((log_(3)(3sqrt(x)))/(3)+(log_(x)(3sqrt(x)))/(3))*log_(3)x^(3))=2

Solve log_(x)3+log_(3)x=log_(sqrt(3))x+log_(3)sqrt(x)+(1)/(2)

x^(log_(sqrt(x))2x)=4

IF log_(6)log_(2)[sqrt(4x+2)]+2sqrt(x)=0, then x=

If x=(2)^((log_(2)3log_(3)4log_(4)5)......log_(19)20),y=5^(log_(2)3)-3^(log_(2)5),z=log_(sqrt(256))sqrt(log_(sqrt(2))4) then value of (x+y).z is

2log_(2)(log_(2)x)+log_((1)/(5))(log_(2)2sqrt(2x))=1

Find the value of log_(4)*log_(2)log sqrt(2)log_(3)(x-21)=0