解方程3log(x)4+2log(4x)4+3log(16x)4=0

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解方程3log‹x›4+2log‹4x›4+3log‹16x›4=0
将真数和对数互换得：3/log₄x+2/log₄4x+3/log₄16x=0
即有3/log₄x+2/(1+log₄x)+3/(2+log₄x)=0
令log₄x=u,则上式变为3/u+2/(1+u)+3/(2+u)=0
去分母得3(1+u)(2+u)+2u(2+u)+3u(1+u)=0
展开化简得4u²+8u+3=(2u+1)(2u+3)=0,故u₁=-1/2；u₂=-3/2.
由log₄x=-1/2,得x₁=4^(-1/2)=1/√4=1/2；
由log₄x=-3/2,得x₂=4^(-3/2)=1/√64=1/8.

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