求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数?
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![求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数?](/uploads/image/z/5423193-9-3.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y+%3D+log10%28x+%26%238722%3B+2%29+and+y+%3D+1+%26%238722%3B+log10%28x+%2B+1%29.%E7%9A%84%E4%BA%A4%E7%82%B9%2C%E4%B8%BA%E4%BB%80%E4%B9%88x-2%E5%92%8Cx%2B1%E6%98%AF%E6%AD%A3%E6%95%B0%3F)
求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数?
求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数?
求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数?
答:
求函数y = log10(x − 2) and y = 1 − log10(x + 1).的交点,为什么x-2和x+1是正数
因为对数函数的真数必须是正数
所以:
x-2>0
x+1>0
否则对数函数没有意义
y = log10(x − 2) = 1 − log10(x + 1)=log10[10/(x+1)]
x-2=10/(x+1)
x^2-x-2=10
x^2-x-12=0
(x-4)(x+3)=0
x=4或者x=-3
因为:x-2>0,x+1>0
所以:x>2
所以:x=-3不符合
综上所述,x=4,y=log10(2)
所以:交点为(4,lg2)