It is currently 18 Nov 2017, 01:44

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 4^4x = 1600, what is the value of (4^x–1)^2?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 Sep 2013
Posts: 29

Kudos [?]: 31 [0], given: 82

Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
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
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:45) correct 30% (02:25) wrong based on 262 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
[Reveal] Spoiler: OA

Kudos [?]: 31 [0], given: 82

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132539 [4], given: 12324

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

### Show Tags

18 Oct 2013, 10:59
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

_________________

Kudos [?]: 132539 [4], given: 12324

Intern
Joined: 10 Sep 2012
Posts: 3

Kudos [?]: 7 [0], given: 26

GMAT Date: 08-27-2013
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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.

Kudos [?]: 7 [0], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132539 [1], given: 12324

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

### Show Tags

20 Oct 2013, 06:06
1
KUDOS
Expert's post
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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: math-number-theory-88376.html
_________________

Kudos [?]: 132539 [1], given: 12324

Senior Manager
Joined: 08 Apr 2012
Posts: 445

Kudos [?]: 79 [0], given: 58

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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

Is there another aproach?What if I don't realize the $$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ - ?

Kudos [?]: 79 [0], given: 58

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1385 [6], given: 136

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

### Show Tags

02 Nov 2013, 23:29
6
KUDOS
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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.

$$4^{(x-1)^2} = [\frac{4^x}{4^1}]^2 = [\frac{4^{2x}}{4^2}]$$ 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 $$t = \frac{10}{4} =\frac{5}{2}$$
_________________

Kudos [?]: 1385 [6], given: 136

Senior Manager
Joined: 08 Apr 2012
Posts: 445

Kudos [?]: 79 [0], given: 58

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.

Kudos [?]: 79 [0], given: 58

Intern
Joined: 16 Feb 2013
Posts: 6

Kudos [?]: 2 [0], given: 9

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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

Hi Bunuel, why isn't (x-1)^2 is not treated like (a-b)^2 formula?

Thanks

Kudos [?]: 2 [0], given: 9

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132539 [1], given: 12324

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

### Show Tags

21 Feb 2014, 00:18
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

Hi Bunuel, why isn't (x-1)^2 is not treated like (a-b)^2 formula?

Thanks

Actually parenthesis were missing there. Edited, it should read: $$(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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.
_________________

Kudos [?]: 132539 [1], given: 12324

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1852

Kudos [?]: 2707 [3], given: 193

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

24 Feb 2014, 01:28
3
KUDOS
One more approach:

Refer Step I to Step VI
Attachment:

power.jpg [ 47.28 KiB | Viewed 2961 times ]

$$4^{4x} = 1600$$

Dividing both sides by $$4^4$$
$$\frac{4^{4x}}{4^4} = \frac{1600}{4^4}$$

$$4^{4x-4} = \frac{100}{16}$$

$$4^{(x-1)^4} = \frac{10^2}{4^2}$$

Square root both sides

$$4^{(x-1)^2} = \frac{10}{4} = \frac{5}{2}$$

_________________

Kindly press "+1 Kudos" to appreciate

Last edited by PareshGmat on 02 Sep 2014, 21:01, edited 1 time in total.

Kudos [?]: 2707 [3], given: 193

Intern
Joined: 07 Jul 2013
Posts: 3

Kudos [?]: [0], given: 7

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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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!

Kudos [?]: [0], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132539 [2], given: 12324

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

### Show Tags

27 Feb 2014, 11:08
2
KUDOS
Expert's post
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

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

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.
_________________

Kudos [?]: 132539 [2], given: 12324

Non-Human User
Joined: 09 Sep 2013
Posts: 15714

Kudos [?]: 281 [0], given: 0

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

### Show Tags

26 Jul 2015, 23:08
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.
_________________

Kudos [?]: 281 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15714

Kudos [?]: 281 [0], given: 0

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

### Show Tags

05 Aug 2016, 22:21
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.
_________________

Kudos [?]: 281 [0], given: 0

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?   [#permalink] 05 Aug 2016, 22:21
Display posts from previous: Sort by

# If 4^4x = 1600, what is the value of (4^x–1)^2?

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.