Question

求下列各等式中的x值.

(1)log₂［log₃(log₄x)］=0;

(2).

Answer 1

解：(1)∵log₂［log₃(log₄x)］=0,∴log₃(log₄x)=1.∴log₄x=3.∴x=4³=64.

(2)首先,x²-1＞0且x²-1≠1,即x＞1或x＜-1且x≠±.

其次，原等式可化為x²-1=2x²-3x+1.

∴x²-3x+2=0.∴x=1或x=2.

又∵x＞1或x＜-1且x≠±,∴x=2.

經檢驗x=2適合等式.