函数y=log(2^2)x-log(2)x的单调递减区间

1个回答

  • 对数底数的幂指数可以化为它的倒数移去做系数,于是

    y=log(2^2)x-log(2)x=[log(2)x] /2 - log(2)x = - [log(2)x] /2

    y=log(a)x在a>1时在(0,+∞)上单调递增,显然2>1,于是

    y=log(2)x在(0,+∞)上单调递增

    若y=f(x)单调递增,则y=kf(x)在k<0时单调递减,显然 -1/2<0,于是

    y = - [log(2)x] /2 在(0,+∞)上单调递减

    即知原函数的单调递减区间为(0,+∞)