" 5."sqrt(x^(2)+y^(2))=log(x^(2)-y^(2))

Number of ordered pair (s) (x,y) satisfying the system of equations 2log(x^(2)+y^(2))-log5=log{2(x^(2)+y^(2))+75}and log((x)/(3))+log(5y) =1+log2, is

y=log[(x+sqrt(x^(2)+a^(2)))/(sqrt(x^(2)+a^(2))-x)]

y = log((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))

y = log((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))

If log_((x-y))(x+y)=5 , then what is the value of log_(x^(2)-y^(2))(x^(2)-2xy + y^(2))?

If x-sqrt(a^(2)-y^(2))=a" log"(a-sqrt(a^(2)-y^(2)))/(y) , show that, (dy)/(dx)=(y)/(sqrt(a^(2)-y^(2)))

If y=log((x+sqrt(x^(2)+a^(2)))/(-x+sqrt(x^(2)+a^(2))))"then "dy/dx=

If y=log[x+sqrt(x^(2)+a^(2))], show that ((x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log{x+sqrt(x^(2)+a^(2))}, prove that: (x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0