# Thread: Why does > have to be flipped?

1. ## Why 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

2. Originally Posted by freswood
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
Hello,

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

3. Originally Posted by earboth

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

EB
Oops I didn't mean to change the numerator to the denominator. But you do need to flip the sign because otherwise it doesn't hold true in the original equation. x has to be less than -1.27 for 0.3^x to be greater than 4.6.

4. Originally Posted by freswood
Oops I didn't mean to change the numerator to the denominator. But you do need to flip the sign because otherwise it doesn't hold true in the original equation. x has to be less than -1.27 for 0.3^x to be greater than 4.6.
Hello,

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

5. 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.