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what do we do with exponents?

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Source: — Problem Solving |
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by parallel_chase » Mon Aug 04, 2008 1:06 am
3^x - 3^x-1 = 162

first thing first factorize 162 = 2*(3)^4


3^x - 3^x-1
3^x - (3^x/3)
(3*3^x - 3^x)/3
[3^x (3-1)]/3

[3^x * 2]/3 = 2*(3)^4

x=5

x(x-1) = 5(5-1)=5*4 =20

Hope this helps.
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by sibbineni » Mon Aug 04, 2008 3:16 am
3^x - 3^x-1 = 162


prime factors of 162=3^4*2

3^x-3^x-1=3^4*2

here apply the formula a^m-n=a^m/a^n

3^x-3^x/3=3^4*2

now take 3^x as common from LHS

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

3^x*2/3=3^4*2

3^x*2=3^4*2*3

3^x=3^4*3

3^x=3^5

x=5

then x(x-1)=

5(5-1)=20

hope this clears up
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by vishubn » Tue Aug 05, 2008 10:18 am
3^x-3^x/3=162
3(3^x)-3^x=162*3

3^x(3-1)162*3
3^x=3^4*3
3^x=3^5
x=5

then x(x-1) =20

Vishu

hope this helps
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