作业帮(log(2)(x))^3-4(log(4)(x))^2+log(16)(x)=0
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(log(2)(x))^3-4(log(4)(x))^2+log(16)(x)=0
(log(2)(x))^3-4(log(4)(x))^2+log(16)(x)=0
(log(2)(x))^3-4(log(4)(x))^2+log(16)(x)=0
令a=log2(x)
log4(x)=lgx/lg4=lgx/2lg2=(1/2)lgx/lg2=(1/2)log2(x)=a/2
同理,log16(x)=lgx/4lg2=a/4
所以a^3-4(a/2)^2+a/4=0
a(a^2-4a+1/4)=0
a^2-4a+1/4=0的根是(4±√15)/2
所以a=0,a=(4±√15)/2
a=log2(x)
x=2^a
所以x=1,x=2^[(4-√15)/2],x=2^[(4+√15)/2]
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(log(2)(x))^3-4(log(4)(x))^2+log(16)(x)=0
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