求解log2 (3X+2)-log4 (X)=3

问题描述:

求解log2 (3X+2)-log4 (X)=3

(26-8√10)/9或(26+8√10)/9

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-...