25 ++ if log(x y/2)=1/2(logx logy) prove that x^2 y^2=6xy 267687

Answer If x^2 y^2 = 7xy, how do you prove that 1/2 (logx logy) = log(xy/3) ^2?

If log(x y/2)=1/2(logx logy) prove that x^2 y^2=6xy-Log b ( x y) = y ∙ log b ( x) The base b logarithm of c is 1 divided by the base c logarithm of b The base b logarithm of x is base c logarithm of x divided by the base c logarithm of b For example, in order to calculate log 2 (8) in calculator, we need to change the base to 10Problem #1 Find x for log 2 (x) log 2 (x3) = 2 Solution Using the product rule log 2 (x∙(x3)) = 2 Changing the logarithm form according to the logarithm definition x∙(x3) = 2 2 Or x 23x4 = 0 Solving the quadratic equation x 1,2 = 3±√(916) / 2 = 3±5 / 2 = 4,1 Since the logarithm is not defined for negative numbers, the answer is x = 4 Problem #2 Find x for log 3