Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If 2^x - 2^(x-2) = 3*2^(13), what is x? [#permalink]
28 Aug 2013, 13:27

I did it a bit differently, but I arrived at the right answer. Here is the way I did it: 2^x - 2^{x-2} = 3* 2^{13} Factor out a 2^x which gives: 2^x(1 - \frac{1}{4}) = 3* 2^{13} Clean up: 2^x(\frac{3}{4}) = 3* 2^{13} At this point I realized that the 4 in the denominator could be factored out so that's what I did: 2^{x-2}(3) = 3* 2^{13} From here you have 2^{x-2} = 2^{13} so x = 15

Can you please explain the red highlighted part? I read other explanations but it wasn't clear. I am unable to understand how did you factor out 2^(x-2)?

Can you please explain the red highlighted part? I read other explanations but it wasn't clear. I am unable to understand how did you factor out 2^(x-2)?

Sure! First notice that 2^{x-2} * 2^{2} = 2^{x} So, we know that 2^{x-2} is a factor of 2^{x}. I am using the product rule for exponents: x^{a}*x^{b}=x^{a+b} It helps to think of this rule in reverse (going from right -> left). What I mean by that is we can also write it as x^{a+b}=x^{a}*x^{b} When I factor out the 2^{x-2} I am really separating 2^{x} into 2^{x-2} * 2^{2}. So, 2^x - 2^{x-2} = 3*2^{13} which becomes 2^{x-2}(2^2-1)= 3*2^{13} after we factor out the 2^{x}.

Re: If 2^x - 2^(x-2) = 3*2^(13), what is x? [#permalink]
09 Sep 2013, 08:30

Quote:

Clean up: 2^x(\frac{3}{4}) = 3* 2^{13} At this point I realized that the 4 in the denominator could be factored out so that's what I did: 2^{x-2}(3) = 3* 2^{13} From here you have 2^{x-2} = 2^{13} so x = 15

It seems that in the bolded step above you could have multiplied both sides by 4/3 thus canceling the 3 from the other side out. You would then be left with 4 or (2*2) or 2^2 in addition to the 2^13 leaving you with the 2^15. Just thought that might be a little quicker.
_________________

Now it's a pretty simple point, but it got silly old me baffled, so i searched up the net and came up with the following explanation. 2^{x-2}(2^2-1)= 3*2^{13}

If from N^x - N^{x-a}, N^{x-a} is factored out we will have: N^{x-a} (N^b - 1) Where b = x - a Example 1 5^8 - 5^5 = 5^5 (5^3 - 1) = 5^5 (125 - 1) = 5^5*124 Example 2 2^x - 2^{x-2} = 2^x (2^2 - 1) = 2^x (4 - 1) = 2^x . 3

Now in Example 2 we don't know the value of the x but we know the difference betweenx andx-2 is 2 therefore,b = 2.

Now it's a pretty simple point, but it got silly old me baffled, so i searched up the net and came up with the following explanation. 2^{x-2}(2^2-1)= 3*2^{13}

If from N^x - N^{x-a}, N^{x-a} is factored out we will have: N^{x-a} (N^b - 1) Where b = x - a Example 1 5^8 - 5^5 = 5^5 (5^3 - 1) = 5^5 (125 - 1) = 5^5*124 [color=#ff0000]Example 2 [b]2^x - 2^{x-2} = 2^x (2^2 - 1) = 2^x (4 - 1) = 2^x . 3[/color][/b]

Now in Example 2 we don't know the value of the x but we know the difference betweenx andx-2 is 2 therefore,b = 2.