求解log2 (3X+2)-log4 (X)=3

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求解log2(3X+2)-log4(X)=3求解log2(3X+2)-log4(X)=3求解log2(3X+2)-log4(X)=3由换底公式log4(x)=log2(x)/log2(4)=log2(

求解log2 (3X+2)-log4 (X)=3
求解log2 (3X+2)-log4 (X)=3

求解log2 (3X+2)-log4 (X)=3
由换底公式log4(x)=log2(x)/log2(4)=log2(x)/[2log2(2)]=(1/2)×log2(x)=log2(√x)
∴log2 (3X+2)-log2(√x)=3
即log2[(3x+2)/√x]=log2(8)
∴(3x+2)/√x=8
令√x=t,t>0
∴(3t²+2)/t=8,推出3t²+2=8t
即3t²-8t+2=0
解得:t=(4-√10)/3或t=(4+√10)/3 (两个解都大于0,满足条件)
∴x=t²=(26-8√10)/9或(26+8√10)/9

(26-8√10)/9或(26+8√10)/9