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If (3)^x - (3)^x-1 = 162, then x(x-1) =? a)12 b)16 c)20 d)30

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If (3)^x - (3)^x-1 = 162, then x(x-1) =? a)12 b)16 c)20 d)30 [#permalink] New post 21 Apr 2007, 15:33
If (3)^x - (3)^x-1 = 162, then x(x-1) =?

a)12
b)16
c)20
d)30
e)81
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Schools: Kellogg School of Management
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 [#permalink] New post 21 Apr 2007, 23:50
3^x - 3^(x-1) = 162

=> 3^(x-1) * ( 3 - 1) = 162

=> 3^(x-1) = 81

=> x-1 = 4

=> x*(x-1) = 20

so C
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Re: A question about power [#permalink] New post 22 Apr 2007, 04:30
GMAT_700 wrote:
If (3)^x - (3)^x-1 = 162, then x(x-1) =?

a)12
b)16
c)20
d)30
e)81


3^(x-1)[3-1]=162

3^(x-1)=81=3^4.

Comparing the powers of 3 we get x-1=4. Therefore x=5. And hence x(x-1)=4*5=20.

Answere C.

Javed.

Cheers!
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Re: A question about power [#permalink] New post 22 Apr 2007, 12:35
GMAT_700 wrote:
If (3)^x - (3)^x-1 = 162, then x(x-1) =?

a)12
b)16
c)20
d)30
e)81


3^(x-1) {3 - 1} = 162
or 3 ^(x-1) = 81 = 3^4
or x - 1 = 4
so x = 5
x(x-1) = 20
Re: A question about power   [#permalink] 22 Apr 2007, 12:35
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If (3)^x - (3)^x-1 = 162, then x(x-1) =? a)12 b)16 c)20 d)30

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