hey guys, i have a question that i need help on.
it says use the "Rule of Four" to verbally, algebraicly, numerically, and graphically solve the problem.
Find all teh real numbers such that: x^2log(sub 3)x<5xlog(sub 3)x
Ok, I have NO IDEA what the rule of four is... but I do have a solution.
There is a on either side, so logically you would divide both sides by that, but when you do so, you have to consider the value of very carefully, if , then you're fine, dividing both sides by gets you:
When you plot the parabola , you can easily see that the solution for is
Now, consider the case when , this only occurs if :
When , LHS = 0, RHS = 0, hence LHS is not less than RHS, which means if you solve , should NOT be a solution.
So the solution to is .
Hope that helps.