设函数f(x)=logax (a>0,a≠1),若f(x1)f(x2)...f(x2008)=8,则f(x1^2)+f(x2^2)+...f(x2008^2)的值为多少.给出具体过程
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![设函数f(x)=logax (a>0,a≠1),若f(x1)f(x2)...f(x2008)=8,则f(x1^2)+f(x2^2)+...f(x2008^2)的值为多少.给出具体过程](/uploads/image/z/683308-28-8.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dlogax+%28a%3E0%2Ca%E2%89%A01%29%2C%E8%8B%A5f%28x1%29f%28x2%29...f%28x2008%29%3D8%2C%E5%88%99f%28x1%5E2%29%2Bf%28x2%5E2%29%2B...f%28x2008%5E2%29%E7%9A%84%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91.%E7%BB%99%E5%87%BA%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B)
设函数f(x)=logax (a>0,a≠1),若f(x1)f(x2)...f(x2008)=8,则f(x1^2)+f(x2^2)+...f(x2008^2)的值为多少.给出具体过程
设函数f(x)=logax (a>0,a≠1),若f(x1)f(x2)...f(x2008)=8,则f(x1^2)+f(x2^2)+...f(x2008^2)的值为多少.给出具体过程
设函数f(x)=logax (a>0,a≠1),若f(x1)f(x2)...f(x2008)=8,则f(x1^2)+f(x2^2)+...f(x2008^2)的值为多少.给出具体过程
应该f(x1)+f(x2)+...+f(x2008)
=loga x1+loga x2+...+loga x2008
=loga x1*x2*.*x2008
=8
所以x1*x2*.*x2008=a^8
所以f(x1^2)+f(x2^2)+...f(x2008^2)
=loga x1²+loga x2²+...+loga x2008²
=2loga x1+2loga x2+...+2loga x2008
=2loga x1*x2*.*x2008
=2loga a^8
=2*8
=16
f(x1^2)+f(x2^2)+...f(x2008^2)=log(ax1^2)+log(ax2^2)+…+log(ax2008^2)
=2log(ax1)+2log(ax2)+…+2log(ax2008)
=2log(ax2*ax2*…*ax2008)【不想乱教,可是,你确定题目没抄错?f(x1)f(x2)...f(x2008)=8这个有没有抄错了?麻烦你再看下题目】
=...
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f(x1^2)+f(x2^2)+...f(x2008^2)=log(ax1^2)+log(ax2^2)+…+log(ax2008^2)
=2log(ax1)+2log(ax2)+…+2log(ax2008)
=2log(ax2*ax2*…*ax2008)【不想乱教,可是,你确定题目没抄错?f(x1)f(x2)...f(x2008)=8这个有没有抄错了?麻烦你再看下题目】
=2f(x1)f(x2)...f(x2008)=16
收起
f(x1)f(x2)...f(x2008)
=loga x1*loga x2*...* loga x2008
=8
f(x1^2)+f(x2^2)+...f(x2008^2)
=loga x1^2 * loga x2^2 *...* loga x2008^2
=(2loga x1) * (2loga x2) *...* (2loga x200...
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f(x1)f(x2)...f(x2008)
=loga x1*loga x2*...* loga x2008
=8
f(x1^2)+f(x2^2)+...f(x2008^2)
=loga x1^2 * loga x2^2 *...* loga x2008^2
=(2loga x1) * (2loga x2) *...* (2loga x2008)
=2^2008* loga x1*loga x2*...* loga x2008
=2^2008*8
=2^2008 * 2^3
=2^2011
应该是这样子吧。。。。
如果答案是16的话
那题就应该是加法 而不是乘法。。。。
收起
应该f(x1)+f(x2)+...+f(x2008)
=loga x1+loga x2+...+loga x2008
=loga x1*x2*....*x2008
=8
所以x1*x2*....*x2008=a^8
所以f(x1^2)+f(x2^2)+...f(x2008^2)
=loga x1²+loga x2²+...+loga x2008²
=2loga x1+2loga x2+...+2loga x2008
=2loga x1*x2*....*x2008
=2loga a^8
=2*8
=16