C2 Swapping round the more than sign in inequalities

Under what conditions when solving an inequality that involves logs does the more than or equal sign swap round?

The inequality sign swaps round in you divide by a negative number.
The log of any number < 0 will be negative

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Reply 2

Mackiemcmasher

Original post by gdunne42

The inequality sign swaps round in you divide by a negative number.
The log of any number < 0 will be negative

Posted from TSR Mobile

Ah ok thank you.

Reply 3

Kevin De Bruyne

You could also think about why it works.

Eg if you have 8>6 then you know that -1 * 8 < -1* 6, which is the same as -8 < -6, so you see that the sign gets flipped around when it's multiplied by a negative number. (And logx is negative for any x less than 1, and log1=0.)