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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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]

Show Tags

28 Aug 2013, 13:27

1

This post received KUDOS

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 \(x = 15\)

I hope that helps.
_________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

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 \(2^{x}\).

Does that help?
_________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

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

Show Tags

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 between\(x\) and\(x-2\) 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 between\(x\) and\(x-2\) is \(2\) therefore,\(b = 2\).

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

Show Tags

28 May 2016, 23:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...