If x > [a negative number] why does the > need to be exchanged with a <? Am I missing something important about the use of < and >?

Eg.

0.3^x > 4.6

x log 0.3 > log 4.6

x > log 4.6 / log 0.3

log 0.3 / log 4.6 is -1.27 so:

x < -1.27

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- Apr 4th 2006, 01:23 AMfreswoodWhy does > have to be flipped?
If x > [a negative number] why does the > need to be exchanged with a <? Am I missing something important about the use of < and >?

Eg.

0.3^x > 4.6

x log 0.3 > log 4.6

x > log 4.6 / log 0.3

log 0.3 / log 4.6 is -1.27 so:

x < -1.27 - Apr 4th 2006, 04:43 AMearbothQuote:

Originally Posted by**freswood**

1. To explain why you have to change the sign < into > (and vice versa) by multipling with a negative number, I'll show you an example:

3 < 5 is true. Now multiply both sides by (-2) and you'll get:

-6 > -10. Because (-10) is smaller then (-6) or in other words (-6) is greater then (-10) you have to change < into >.

2. This fraction (log 4.6 / log 0.3) is not the same as (log 0.3 / log 4.6) but your result is correct. But you don't have to change the ">"-sign because you don't multiply**both**sides of your inequality by a negative number.

So the result is:

$\displaystyle x > \frac{\log{4.6}}{\log{.3}} \approx -1.27$

Greetings

EB - Apr 4th 2006, 01:38 PMfreswoodQuote:

Originally Posted by**earboth**

- Apr 5th 2006, 12:22 AMearbothQuote:

Originally Posted by**freswood**

you're right. That's because log(0.3) = -0.5228...

So you actually divide by a negative number and then you have to change the ">"-sign. Sorry that I made such a stupid mistake!

Greetings

EB - Apr 5th 2006, 01:45 AMfreswood
That makes sense now. Thanks for your help! I have a SAC (School Assessed Coursework) coming up with this in it which counts towards my year 12 grade.