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Exponents question

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Manager
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Joined: 24 Jun 2009
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Exponents question [#permalink]

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New post 09 Aug 2009, 17:34
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\(5^2^1*4^1^1=2*10^n\)
What does n equal?

Kudos [?]: 93 [0], given: 2

Senior Manager
Senior Manager
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Joined: 20 Mar 2008
Posts: 452

Kudos [?]: 133 [0], given: 5

Re: Exponents question [#permalink]

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New post 09 Aug 2009, 18:03
shanewyatt wrote:
\(5^2^1*4^1^1=2*10^n\)
What does n equal?


or, 5^21. 2^21. 2 = 2.10^n
or, 2.10^21 = 2.10^n

n = 21

Kudos [?]: 133 [0], given: 5

Manager
Manager
avatar
Joined: 24 Jun 2009
Posts: 58

Kudos [?]: 93 [0], given: 2

Re: Exponents question [#permalink]

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New post 09 Aug 2009, 18:27
Jivana wrote:
shanewyatt wrote:
\(5^2^1*4^1^1=2*10^n\)
What does n equal?


or, 5^21. 2^21. 2 = 2.10^n
or, 2.10^21 = 2.10^n

n = 21



How does \(4^1^1\) become \(2*2^2^1\)? Can you break that down?


Another exponents question:
\(2^x-2^x^-^2=3(2^1^3)\)

Kudos [?]: 93 [0], given: 2

Senior Manager
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Affiliations: ACA, CPA
Joined: 26 Apr 2009
Posts: 433

Kudos [?]: 96 [0], given: 41

Location: Vagabond
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WE 1: Big4, Audit
WE 2: Banking
Re: Exponents question [#permalink]

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New post 09 Aug 2009, 20:21
shanewyatt

4^11 = 2^2^11

We then multiply the 2 exponents (2*11) to give us 22
So it ends up as 2^22

Hope this helps
_________________

If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

Kudos [?]: 96 [0], given: 41

Senior Manager
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Posts: 452

Kudos [?]: 133 [0], given: 5

Re: Exponents question [#permalink]

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New post 09 Aug 2009, 20:21
1st one: 4^11 = 2^22 = 2. 2^21

2^x - 2^(x-2) = 3(2^13)

LHS:
2^x - 2^x / 2^2
=2^x ( 1 - 1 / 2^2)
=2^x (4-1)/4
=2^x . 3 / 4
=3.2^(x-2)

Therefore: x- 2 = 13.
or, x = 15.

Last edited by Jivana on 09 Aug 2009, 20:53, edited 1 time in total.

Kudos [?]: 133 [0], given: 5

Senior Manager
Senior Manager
User avatar
Affiliations: ACA, CPA
Joined: 26 Apr 2009
Posts: 433

Kudos [?]: 96 [0], given: 41

Location: Vagabond
Schools: BC
WE 1: Big4, Audit
WE 2: Banking
Re: Exponents question [#permalink]

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New post 09 Aug 2009, 20:28
shanewyatt wrote:


Another exponents question:
\(2^x-2^x^-^2=3(2^1^3)\)


What is the question... does it ask to solve for x?
_________________

If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

Kudos [?]: 96 [0], given: 41

Senior Manager
Senior Manager
User avatar
Affiliations: ACA, CPA
Joined: 26 Apr 2009
Posts: 433

Kudos [?]: 96 [0], given: 41

Location: Vagabond
Schools: BC
WE 1: Big4, Audit
WE 2: Banking
Re: Exponents question [#permalink]

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New post 09 Aug 2009, 20:41
\(2^x - 2^x-2 = 3*(2^13)

= 2^x-2 (2^2-1) = 3*(2^13)
= 2^x-2*(3) = 3*(2^13)
= 2^x-2 = (2^13)
x = 15\)
_________________

If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

Kudos [?]: 96 [0], given: 41

Re: Exponents question   [#permalink] 09 Aug 2009, 20:41
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