log(x)2×log(2x)2=log(4x)2
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log(x)2×log(2x)2=log(4x)2
关于x的方程k*9^x-3k*3^x+6(k-5)=0在[0,2]内有解,求实数k的取值范围,再问一道,嘻嘻,
关于x的方程k*9^x-3k*3^x+6(k-5)=0在[0,2]内有解,求实数k的取值范围,再问一道,嘻嘻,
用换底公式:log(a)b=lgb/lga
log(x)2=lg2/lgx,log(2x)2=lg2/lg(2x)=lg2/(lg2+lgx),log(4x)2=lg2/lg(4x)=lg2/(2lg2+lgx)
所以 (lg2/lgx)×[lg2/(lg2+lgx)]=lg2/(2lg2+lgx)
化简,得:(lgx)²=2(lg2)²
所以lgx=±√2*lg2=lg[2^(±√2)
所以x=2^(±√2)
log(x)2=lg2/lgx,log(2x)2=lg2/lg(2x)=lg2/(lg2+lgx),log(4x)2=lg2/lg(4x)=lg2/(2lg2+lgx)
所以 (lg2/lgx)×[lg2/(lg2+lgx)]=lg2/(2lg2+lgx)
化简,得:(lgx)²=2(lg2)²
所以lgx=±√2*lg2=lg[2^(±√2)
所以x=2^(±√2)
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x=log a 2
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