Question

0.8²，2^0.8，log_0.82，log₂0.8按照从小到大的顺序排列为______．

Answer 1

∵log20.8=log2

4

5

=2-log25且2=log₂⁴＜log₂⁵＜log₂⁸=3
∴-1＜2-log₂⁵＜0
∴-1＜log₂^0.8＜0
∴log_0.8²=

1

log20.8

＜-1＜log₂^0.8＜0
∵0＜0.8＜1
∴2^0.8＞1
∵0.8²=0.64＜1
∴0＜0.8²＜2^0.8
∴2^0.8＞0.8²＞log₂^0.8＞log_0.8²，
故答案为2^0.8＞0.8²＞log₂^0.8＞log_0.8²