Sachin9 wrote:

If x is an integer, is 4^x < 3^(x+1)?

1)x is positive..

I used x=1/2,1,2 to plug in.. and I found 1 is sufficient.. but I didn't use 4 to plug in which yields no to the prompt..

How to determine what nos to plug in and when to stop plugging in?

Please help.

Regards,

Sach

There are two ways you can use:

1. Use logic/algebra instead of plugging in numbers. It's tough to prove something using numbers. It's easier to disprove.

Is 4^x < 3^(x+1)?

Is (4/3)^x < 3?

4/3 is greater than 1. When you raise it to a high power, it will take a big enough value. There is no reason it should stay less than 3. When you raise 1 to a power, it stays 1. When you raise a number less than 1 to a positive integral power, the number becomes even lesser. These are some number properties you need to work through and be comfortable with.

2. Look for the transition point.

Find out where it will be equal. Then the behavior will be different on either side of the transition point (as done in the post above)

I have discussed these two methods in another question. Check it out here:

how-to-stop-searching-for-values-to-prove-a-statement-127787.html#p1047350Remember, you cannot shut your mind and just plug in numbers and get your answer. If it were so easy, everyone would have scored Q51. The point is that you need to always keep your mind on alert and use logic even if you are using number plugging.

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