若5^x+5^(x+1)+5^(x+2)=31/25,求x的值

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若5^x+5^(x+1)+5^(x+2)=31/25,求x的值
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若5^x+5^(x+1)+5^(x+2)=31/25,求x的值
若5^x+5^(x+1)+5^(x+2)=31/25,求x的值

若5^x+5^(x+1)+5^(x+2)=31/25,求x的值
5^x+5^(x+1)+5^(x+2)
=5^x（1+5+25）
=31×5^x=31/25
故5^x=1/25=5^-2
所以x=-2

-2

令a=5^x
则5^(x+1)=5^x*5^1=5a
5^(x+2)=5^2*a=25a
所以a+5a+25a=31/25
a=1/25
5^x=1/25=5^(-2)
x=-2

5^x+5^(x+1)+5^(x+2)=31/25,
5^x+5*5^x+25*5^x=31/25
31*5^x=31/25,
5^x=5^(-2)
x=-2

5^x+5^(x+1)+5^(x+2)=5^x *（1+5+25）=5^x * 31 = 31/25
所以5^x=1/25
所以x=-2

也可以导数方法做的

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