log[b]x/log[b]y=x/y meaning log to base b of x divided by log to the same base of y=x/y. What is the relationship between b, x and y?
Cross-multiply: ylog[b]x=xlog[b]y, so log[b]x^y=log[b]y^x and x^y=y^x or x=y^(x/y) because, if logA=logB then A=B, when the base of the log is the same. So x=y is a solution, because x^x=x^x. The base can be any base and x, y cannot equal 1, because the original equation would make the logs zero, and we can't divide zero by zero.