为什么log2((x+1)²/x)=log2(x+1/x+2)这是原题:设函数f(x)=log2x-2log2(x+1),则f(x)的定义域是多少?最大值是多少?定义域x>0且x+1>0∴x>0f(x)=log2x-2log2(x+1)=log2x-log2(x+1)²=log2(x/(x+1)²)【=-log2((
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![为什么log2((x+1)²/x)=log2(x+1/x+2)这是原题:设函数f(x)=log2x-2log2(x+1),则f(x)的定义域是多少?最大值是多少?定义域x>0且x+1>0∴x>0f(x)=log2x-2log2(x+1)=log2x-log2(x+1)²=log2(x/(x+1)²)【=-log2((](/uploads/image/z/7053892-52-2.jpg?t=%E4%B8%BA%E4%BB%80%E4%B9%88log2%EF%BC%88%28x%2B1%29%26%23178%3B%2Fx%EF%BC%89%3Dlog2%28x%2B1%2Fx%2B2%29%E8%BF%99%E6%98%AF%E5%8E%9F%E9%A2%98%EF%BC%9A%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dlog2x-2log2%28x%2B1%29%2C%E5%88%99f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E6%98%AF%E5%A4%9A%E5%B0%91%EF%BC%9F%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91%EF%BC%9F%E5%AE%9A%E4%B9%89%E5%9F%9Fx%3E0%E4%B8%94x%2B1%3E0%E2%88%B4x%3E0f%28x%29%3Dlog2x-2log2%28x%2B1%29%3Dlog2x-log2%28x%2B1%29%26%23178%3B%3Dlog2%EF%BC%88x%2F%28x%2B1%29%26%23178%3B%EF%BC%89%E3%80%90%3D-log2%EF%BC%88%28)
为什么log2((x+1)²/x)=log2(x+1/x+2)这是原题:设函数f(x)=log2x-2log2(x+1),则f(x)的定义域是多少?最大值是多少?定义域x>0且x+1>0∴x>0f(x)=log2x-2log2(x+1)=log2x-log2(x+1)²=log2(x/(x+1)²)【=-log2((
为什么log2((x+1)²/x)=log2(x+1/x+2)
这是原题:设函数f(x)=log2x-2log2(x+1),则f(x)的定义域是多少?最大值是多少?
定义域
x>0且x+1>0
∴x>0
f(x)=log2x-2log2(x+1)
=log2x-log2(x+1)²
=log2(x/(x+1)²)
【=-log2((x+1)²/x)
=-log2(x+1/x+2)】 “问这一步!”
为什么log2((x+1)²/x)=log2(x+1/x+2)这是原题:设函数f(x)=log2x-2log2(x+1),则f(x)的定义域是多少?最大值是多少?定义域x>0且x+1>0∴x>0f(x)=log2x-2log2(x+1)=log2x-log2(x+1)²=log2(x/(x+1)²)【=-log2((
log2((x+1)²/x)=log2[(x^2+2x+1)/x]=log2[(x^2/x)+(2x/x)+1/x]=log2(x+1/x+2)
(注示: (x+1)²=x²+2x+1;因为分母为x,所以同除以x得:x+1/x+2)
=-log2(x+1/x+2) (以下用的是均值不等式)
<=-log2 (2√(x*/1x) +2) (x=1/x,即x=1时取等号)
<=-log2 (2+2)
<=-2