Jun 16 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score. Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Sep 2013
Posts: 27
Location: United States
Concentration: Finance, General Management
GMAT Date: 10252013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)

If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
18 Oct 2013, 10:52
Question Stats:
68% (02:14) correct 32% (02:51) wrong based on 242 sessions
HideShow timer Statistics
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? A. 40 B. 20 C. 10 D. 5/2 E. 5/4
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
18 Oct 2013, 10:59
Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D.
_________________




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 608

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
02 Nov 2013, 23:29
ronr34 wrote: Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Is there another aproach?What if I don't realize the \(4^{4x} = 1600\) > \(4^{2x} = 40\)  ? I think what Bunuel did is the easiest approach. However, if you are worried that this might not strike you, start with the unknown entity. \(4^{(x1)^2} = [\frac{4^x}{4^1}]^2 = [\frac{4^{2x}}{4^2}]\) and let \(t = [\frac{4^{2x}}{4^2}]\) Now, given that \(4^{4x} = 1600.\) Thus,\(t^2 = [\frac{4^{4x}}{4^4}]\) =\([\frac{1600}{16*16}] = [\frac{100}{16}]\)and \(t = \frac{10}{4} =\frac{5}{2}\)
_________________




Intern
Joined: 10 Sep 2012
Posts: 2
GMAT Date: 08272013
GPA: 3.5
WE: Investment Banking (Energy and Utilities)

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
20 Oct 2013, 06:00
Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. I am getting the answer as 5/4.. I just can figure out what have i missed? 4^4 . 4^x = 4^3 . 5^2 4^2x = 25 now, 4^2x/4^2 = 25/16 =5/4.



Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
20 Oct 2013, 06:06
chitrasekar2k5 wrote: Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. I am getting the answer as 5/4.. I just can figure out what have i missed? 4^4 . 4^x = 4^3 . 5^2 4^2x = 25 now, 4^2x/4^2 = 25/16 =5/4. \(4^{4}*4^x=4^{4+x}\) not \(4^{4x}\): \(a^n*a^m=a^{n+m}\) Check here for more: mathnumbertheory88376.html
_________________



Senior Manager
Joined: 08 Apr 2012
Posts: 344

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
02 Nov 2013, 03:35
Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Is there another aproach?What if I don't realize the \(4^{4x} = 1600\) > \(4^{2x} = 40\)  ?



Senior Manager
Joined: 08 Apr 2012
Posts: 344

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
03 Nov 2013, 01:30
Great!!! Thanks a lot.



Intern
Joined: 16 Feb 2013
Posts: 6

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
20 Feb 2014, 16:43
Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi Bunuel, why isn't (x1)^2 is not treated like (ab)^2 formula? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
21 Feb 2014, 00:18
streamingline wrote: Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \(4^{(x1)^2}=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi Bunuel, why isn't (x1)^2 is not treated like (ab)^2 formula? Thanks Actually parenthesis were missing there. Edited, it should read: \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus: \(a^m^n=a^{(m^n)}\) and not \((a^m)^n\), which on the other hand equals to \(a^{mn}\). So: \((a^m)^n=a^{mn}\); \(a^m^n=a^{(m^n)}\) and not \((a^m)^n\). Hope it helps.
_________________



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1798
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
Updated on: 02 Sep 2014, 21:01
One more approach: Refer Step I to Step VI Attachment:
power.jpg [ 47.28 KiB  Viewed 4901 times ]
\(4^{4x} = 1600\) Dividing both sides by \(4^4\) \(\frac{4^{4x}}{4^4} = \frac{1600}{4^4}\) \(4^{4x4} = \frac{100}{16}\) \(4^{(x1)^4} = \frac{10^2}{4^2}\) Square root both sides \(4^{(x1)^2} = \frac{10}{4} = \frac{5}{2}\) Answer = D
_________________
Kindly press "+1 Kudos" to appreciate
Originally posted by PareshGmat on 24 Feb 2014, 01:28.
Last edited by PareshGmat on 02 Sep 2014, 21:01, edited 1 time in total.



Intern
Joined: 07 Jul 2013
Posts: 3

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
27 Feb 2014, 09:32
Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi Bruno, thank you for posting all these answers. They are a great tool!! Quick question though. I just want to confirm the steps of \(4^{4x} = 1600\) TO \(4^{2x} = 40\)  Do you just squareroot the two sides? \(\sqrt{4^{4x}} = \sqrt{1600}\) So the base, 4, doesn't change, only the ^4x gets rooted to ^2x. Is that right? Thank you again!



Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
27 Feb 2014, 11:08
hieracity wrote: Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi Bruno, thank you for posting all these answers. They are a great tool!! Quick question though. I just want to confirm the steps of \(4^{4x} = 1600\) TO \(4^{2x} = 40\)  Do you just squareroot the two sides? \(\sqrt{4^{4x}} = \sqrt{1600}\) So the base, 4, doesn't change, only the ^4x gets rooted to ^2x. Is that right? Thank you again! Yes: \(4^{4x} = 1600\); \((4^{2x})^2 = 40^2\); \(4^{2x} =40\). Hope it's clear.
_________________



VP
Joined: 09 Mar 2018
Posts: 1004
Location: India

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
04 Feb 2019, 23:21
Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi BunuelWhat is wrong in this approach?? Can you please share your thoughts on this. If 4^(4x) = 1600 \(2^{8x} = 2^6 * 5^2\) 8x = 6 x= 3/4 Now [4^(x–1)]^2 [2^2(x–1)]^2 [ 2 ^(2x 2)] ^ 2 (substituted the value of x= 3/4 here) [2^1/2]^2 1/2 Here i was able to guess D, because the denominator was 2 and somehow that 5 has come to the numerator as it is the root of 25.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.



Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
05 Feb 2019, 00:06
KanishkM wrote: Bunuel wrote: Yash12345 wrote: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40 B. 20 C. 10 D. 5/2 E. 5/4 \(4^{4x} = 1600\) > \(4^{2x} = 40\)  \((4^{(x1)})^2=4^{2(x1)}=4^{2x2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}\). Answer: D. Hi BunuelWhat is wrong in this approach?? Can you please share your thoughts on this. If 4^(4x) = 1600 \(2^{8x} = 2^6 * 5^2\) 8x = 6 x= 3/4Now [4^(x–1)]^2 [2^2(x–1)]^2 [ 2 ^(2x 2)] ^ 2 (substituted the value of x= 3/4 here) [2^1/2]^2 1/2 Here i was able to guess D, because the denominator was 2 and somehow that 5 has come to the numerator as it is the root of 25. The red part is not correct. If you could get 8x = 6 from here \(2^{8x} = 2^6 * 5^2\), then you'd get 1=5^2, which is obviously not correct. The point is that you cannot equate the powers there. Some power of 2 (2^(8x)) to be equal to 2^6 * 5^2, x must be some irrational number.
_________________



VP
Joined: 09 Mar 2018
Posts: 1004
Location: India

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
Show Tags
05 Feb 2019, 00:14
Bunuel wrote: KanishkM wrote: Hi BunuelWhat is wrong in this approach?? Can you please share your thoughts on this. If 4^(4x) = 1600 \(2^{8x} = 2^6 * 5^2\) 8x = 6 x= 3/4. The red part is not correct. If you could get 8x = 6 from here \(2^{8x} = 2^6 * 5^2\), then you'd get 1=5^2, which is obviously not correct. The point is that you cannot equate the powers there. Some power of 2 (2^(8x)) to be equal to 2^6 * 5^2, x must be some irrational number. Thank you Bunuel, I think i got your point So basically if i had to get a value of x, i need to find a value which will completely consume RHSWhich now i realize, will be a cumbersome task.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.




Re: If 4^4x = 1600, what is the value of (4^x–1)^2?
[#permalink]
05 Feb 2019, 00:14






