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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
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Re: If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink] New post 15 Jan 2015, 21:04
\(3^x - 3^{(x-1)} = 162\)

\(3^x (1 - \frac{1}{3}) = 162\)

\(3^x * \frac{2}{3} = 162\)

\(3^x = 3^5\)

x = 5; x-1 = 4

x(x-1) = 5*4 = 20
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Re: If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink] New post 15 Jan 2015, 23:17
Expert's post
Hi All,

If you're not an expert at tougher exponent rule questions such as this, you can sometimes get to the answer with a bit of "brute force", even without knowing the exact exponent rules involved in the prompt. Here's how:

This question involves 3 raised to different "powers"; you can calculate them rather easily...

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243

3^X and 3^(X-1) are consecutive powers of 3.
We're told that 3^X - 3^(X-1) = 162, so we just need to find 2 consecutive multiples of 3 that differ by 162.

Notice how...
3^5 - 3^4 =
243 - 81 =
162

This is EXACTLY what we're looking for.

X = 5
(X-1) = 4

So....(X)(X-1) = (5)(4) = 20

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Rich
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Re: If 3 x - 3 x-1 = 162 , then x(x-1)=   [#permalink] 15 Jan 2015, 23:17
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