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
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,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