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If 3 x - 3 x-1 = 162 , then x(x-1)=

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If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink] New post 23 Apr 2008, 04:11
If 3x - 3x-1 = 162, then x(x-1)=?
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Re: Math question \ powers and equations [#permalink] New post 23 Apr 2008, 04:29
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stinger wrote:
If 3x - 3x-1 = 162, then x(x-1)=?


This one was kinda nasty. IM not the best with exponent problems

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

Factor out the 162.

3^x-3^(x-1)=3^4*2 ---> Divide by 3^4 --> 3^x/3^4 - 3^(x-1)/3^4 ---> 3^x-4 - 3^x-5 =2

Now from here I just plugged in a few numbers for X. You can see this wont be very tough b/c -3^x-5 in most cases is going to cancel out 3^x-4 and create a negative number.

Only when x=5 does 3^x-4- 3^x-5 =2. ---> 3^1 - 3^0 = 2.

so now 5(5-1) = 20.
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Re: Math question \ powers and equations [#permalink] New post 23 Apr 2008, 05:24
3^x-3^(x-1)=3^(x-1)*(3-1) -> 3^(x-1) = 162/2 =81
->x=5
Re: Math question \ powers and equations   [#permalink] 23 Apr 2008, 05:24
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