Problem Solving

I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!

uncbeers wrote:I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!

Ur Absolutely right !!!

You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)

I think the 5^2 was a typo but either way thanks for confirming and correcting.

THank you to Ian as well for the additional info-all is clear and rally helps to look at it and figure that out.

AlaaQasem wrote:You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)

Why is it a 3 and not a 2?