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AK79
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GMATPrep PS Exponents 27 Aug 2007, 12:50
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Hello all,

Doing last minute prep (test is on Sat.)

Needed help with this problem from the GMATPrep:

2^x - 2^x-2 = 3(2^13) Solve for x.

I got to:

2^x(1-2^-2) = 3(2^13) but am stuck.

Thanks all. :-D

(The ans is 15)



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KillerSquirrel
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GMATPrep PS Exponents 27 Aug 2007, 13:02
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2^x - 2^(x-2) = 3*(2^13)

2^x*(1-2^-2) = 3*(2^13)

2^x*(1-1/4) = 3*(2^13)

2^x*(3/4) = 3*(2^13)

3*2^x/4 = 3*(2^13)

3*2^x = 4*3*(2^13)

3*2^x = 2^2*3*2^13

3*2^x = 3*2^15

x = 15

:-D
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AK79
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GMATPrep PS Exponents 27 Aug 2007, 14:50
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Ah, gotcha... Thanks mate... :)
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GMATBLACKBELT
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GMATPrep PS Exponents 27 Aug 2007, 15:32
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AK79
Hello all,

Doing last minute prep (test is on Sat.)

Needed help with this problem from the GMATPrep:

2^x - 2^x-2 = 3(2^13) Solve for x.

I got to:

2^x(1-2^-2) = 3(2^13) but am stuck.

Thanks all. :-D

(The ans is 15)
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2^x-2^x-2=(2^2-1)(2^13)

2^x-2^x-2=2^15-2^13...

ok so 2^x-2^x-2... x must be 15 to equal wuts on the other side
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Sumithra Sen
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GMATPrep PS Exponents 28 Aug 2007, 13:24
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Answer 15. Good explanation Killersquirrel.
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PaulyPrime
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GMATPrep PS Exponents 29 Aug 2007, 14:31
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KillerSquirrel,

Can you show me how you went from

1) 2^x - 2^(x-2) = 3*(2^13) to

2) 2^x*(1-2^-2) = 3*(2^13)?

I'm particularly confused about how you factored a 1 out of 2^(x-2) to get 1-2^-2.

Thanks in advance!
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AK79
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GMATPrep PS Exponents 29 Aug 2007, 15:25
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Pauly,

Just to chime in on the quandry:

1) 2^x - 2^(x-2) = 3*(2^13) to

2) 2^x*(1-2^-2) = 3*(2^13)?

2^x is the common factor in the equation. Let's use the following as an example.

Rewrite the initial stem as: 2^x - (2^x)(2^-2)

Working it out using the exponent properties (when multiplying exponents, add them together when the base is the same), we get 2^x-2 for the second part.

Factoring out the 2^x leaves you with: 1 - 2^-2.

Hope this helps, didn't meant to step on your toes Killer :-D (feel free to jump in and add as necessary!)
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subhen
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GMATPrep PS Exponents 29 Aug 2007, 15:25
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This can be solved in 3 steps if you factor out 2^x-2

2^x - 2^x-2 = 3 (2^13)
implies 2^(x-2)(2^2 - 1) = 3. 2^13
3.2^(x-2)=3.2^13
implies x-2=13 implies x=15
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KillerSquirrel
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GMATPrep PS Exponents 30 Aug 2007, 12:55
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AK79
Pauly,

Just to chime in on the quandry:

1) 2^x - 2^(x-2) = 3*(2^13) to

2) 2^x*(1-2^-2) = 3*(2^13)?

2^x is the common factor in the equation. Let's use the following as an example.

Rewrite the initial stem as: 2^x - (2^x)(2^-2)

Working it out using the exponent properties (when multiplying exponents, add them together when the base is the same), we get 2^x-2 for the second part.

Factoring out the 2^x leaves you with: 1 - 2^-2.

Hope this helps, didn't meant to step on your toes Killer :-D (feel free to jump in and add as necessary!)
Show more


very good explanation !

:-D



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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Thank you for understanding, and happy exploring!
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