Solve: `log_3(sqrt(x)+|sqrt(x)-1|)=log_9(4sqrt(x)-3+4|sqrt(x)-1|)`

Solve for x: log_(sqrt3) (x+1) = 2

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

Solve log_(5)sqrt(7x-4)-1/2=log_5sqrt(x+2)

Solve : (sqrt(4x+1)+sqrt(x+3))/(sqrt(4x+1)-sqrt(x+3))=(4)/(1)

Solve foe x in R sqrt(x+8+6 sqrt(x-1))-sqrt(x+3+4sqrt(x-1))=1 .

Find the sum of the squares of all the real solution of the equation 2log_((2+sqrt3)) (sqrt(x^2+1)+x)+log_((2-sqrt3)) (sqrt(x^2+1)-x)=3

Find the sum of the squares of all the real solution of the equation 2log_((2+sqrt3)) (sqrt(x^2+1)+x)+log_((2-sqrt3)) (sqrt(x^2+1)-x)=3

Find the sum of the squares of all the real solution of the equation 2log_((2+sqrt3)) (sqrt(x^2+1)+x)+log_((2-sqrt3)) (sqrt(x^2+1)-x)=3

Solve : (log_(2)(x-4)+1)/(log_(sqrt2)(sqrt(x+3)-sqrt(x-3))) = 1 .