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Simplify Logarithms?

發問:

[log (x^2 )y - log xy ] / [ log x y^2 - log x^2 y^2} 更新: Please show clear STEPS!! Thanks!!

最佳解答:

[log (x^2 )y - log xy ] / [ log x y^2 - log x^2 y^2] ={log [(x^2 y)/(xy)]} / {log [(xy^2)/(x^2 y^2)]} = log x / log(1/x) = log x / ( - log x ) = - 1

其他解答:

log x^2y - log xy = log (x^2y/xy) = log x. log xy^2 - log x^2y^2 = log (xy^2/x^2y^2) = log 1/x = - log x. So answer = log x/-log x = -1.