Question:The value of log`_(.01) (1000) is :` 

A `1/3` 
B `-1/3` 
C `3/2` 
D `- 3/2` 

+ Answer
D 

+ Explanation
Let log`_(.01) (1000) =m.`

Then,`(.01)^m = 100 ⇔ (1/100)^m`

`= 100`

`⇔ (1/10^2)^m`

`= 10^3 ⇔ (10 ^-2)^m`

`= 10^3 ⇔ 10^-2m`

`= 10^3.`

`:. - 2m = 3 or m`

`= - 3/2`

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