If `x^2 + y^2 = 6xy` , prove that 2 log (x + y) = logx + logy + 3 log 2

If x^(2)+y^(2) = 6xy , then prove that 2log(x+y) = log x + logy + 3log2 .

x^(2) + y^(2)= 25xy , then prove that 2 log(x + y) = 3log3 + logx + logy.

If y= x^(y^x) , prove that y_1 = (ylogy(1+x logx logy)/(x log x (1-xlogy))

If y=x^(y^(x)) , prove that, (dy)/(dx)=(y log y(1+x logx log y))/(x logx(1-x logy)) .

y = c log x - 2

We can write log"" x/y = log (x.y^(-1 )) Can you prove that log"" x/y = log x - logy using product and power rules.

If x^(y) =e^(x-y) , prve that , (dy)/(dx) =(logx)/((log ex)^(2)) .

If y log x= x-y , prove that (dy)/(dx)= (log x)/((1+log x)^(2))

If x^2 + y^2 = log(xy) , find dy/dx .

If x^(logy)=logx , prove that, (x)/(y).(dy)/(dx)=(1-logx log y)/((log x)^(2))