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# Inequality watch

1. If ,

How do you prove that ?

Any hints? Thanks.
2. Um, take logs to base |a|?
3. (Original post by DFranklin)
Um, take logs to base |a|?

I forgot the fact that .
However, why is the inequality sign reversed?

Thanks.
4. It shouldn't be, I think.
5. (Original post by melbss01)
If ,

How do you prove that ?

Any hints? Thanks.
If 10 squared is less than 1000, how can 2 be greater than Log 1000, which is 3?
6. (Original post by stevencarrwork)
If 10 squared is less than 1000, how can 2 be greater than Log 1000, which is 3?
i was thinking that

i think the question has been written wrong and the inequality should be the same way round as the initial inequality sign

EDIT: i was trying to think of a good example but you beat me to it
7. (Original post by Anon the 7th)
i was thinking that

i think the question has been written wrong and the inequality should be the same way round as the initial inequality sign

EDIT: i was trying to think of a good example but you beat me to it
Yup. Since , it is an increasing function, it's true that . If you let (just to avoid confusion), then:

(I'm sure you can accept that if , it doesn't work.)

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