Question

比较下列各组数的大小．

(1)log₂π与log₂0.9；(2)log₂0.3与log_0.2 0.3；

(3)log_0.76，0.7⁶与6^0.7.

Answer 1

解：(1)∵函数y＝log₂x在(0，＋∞)上是增函数，

π>0.9，∴log₂π>log₂0.9.

(2)∵log₂0.3<log₂1＝0，log_0.20.3>log_0.21＝0，

∴log₂0.3<log_0.20.3.

(3)∵6^0.7>6⁰＝1，0<0.7⁶<0.7⁰＝1，

log_0.76<log_0.71＝0，

∴6^0.7>0.7⁶>log_0.76.