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

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

If x = e^(x/y) , prove that (dy)/(dx) = (x-y)/(x log x) .

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) = a^(x) , prove that (dy)/( dx) = ( x log _(e) a -y)/( x log_(e) x)

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

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)7.5

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)15

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)6750