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by diebeatsthegmat » Sat Oct 02, 2010 10:36 pm
vongdn wrote:3^x - 3^(x-1) = 162, then x(x-1) = ?

How do I find x to solve the final question?
3^x-3^(x-1)=3*3^x-3^x=2*3^x=162=2*3^4
thus x=4
so 4*3=12
and about the question you poster later
2+2^1+...+2^8=?
2+2^1=2+2=4 =2^2
2^2+2^2=4+4=8=2^3
you do the same till 2^8+2^8=2^9
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by gmatmachoman » Sat Oct 02, 2010 10:54 pm
diebeatsthegmat wrote:
vongdn wrote:3^x - 3^(x-1) = 162, then x(x-1) = ?

How do I find x to solve the final question?
3^x-3^(x-1)=3*3^x-3^x=2*3^x=162=2*3^4
thus x=4
so 4*3=12
and about the question you poster later
2+2^1+...+2^8=?
2+2^1=2+2=4 =2^2
2^2+2^2=4+4=8=2^3
you do the same till 2^8+2^8=2^9
3^x - 3^(x-1) = 162,

3^X ( 1- 1/3)



3^X ( 2/3) = 162

X = 5

x(x-1) = = 5* 4 = 20
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by vongdn » Sat Oct 02, 2010 10:54 pm
diebeatsthegmat wrote:
vongdn wrote:3^x - 3^(x-1) = 162, then x(x-1) = ?

How do I find x to solve the final question?
3^x-3^(x-1)=3*3^x-3^x=2*3^x=162=2*3^4
thus x=4
so 4*3=12
and about the question you poster later
2+2^1+...+2^8=?
2+2^1=2+2=4 =2^2
2^2+2^2=4+4=8=2^3
you do the same till 2^8+2^8=2^9
Thanks for the reply, but I think the answer is x=5 in the first problem.

Maybe it's hard to see through typing, but I don't see how (3^x) - 3^(x-1) = 3 * 3^x - 3^x

thanks
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by vongdn » Sat Oct 02, 2010 11:40 pm
gmatmachoman wrote:
diebeatsthegmat wrote:
vongdn wrote:3^x - 3^(x-1) = 162, then x(x-1) = ?

How do I find x to solve the final question?
3^x-3^(x-1)=3*3^x-3^x=2*3^x=162=2*3^4
thus x=4
so 4*3=12
and about the question you poster later
2+2^1+...+2^8=?
2+2^1=2+2=4 =2^2
2^2+2^2=4+4=8=2^3
you do the same till 2^8+2^8=2^9
3^x - 3^(x-1) = 162,

3^X ( 1- 1/3)



3^X ( 2/3) = 162

X = 5

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

Hi, thanks....


How did you go from

3^x - 3^(x-1) = 3^X ( 1- 1/3)
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by gmatmachoman » Sun Oct 03, 2010 1:35 am
How did you go from

3^x - 3^(x-1) = 3^X ( 1- 1/3)


Step 1 :
3^(x-1)
= 3^x / 3^1 ( formula x^a/ x^b = x^ (a-b) )

= 3^x / 3

step 2:

taking 3 ^x common

3^x - 3^(x-1) = 3^X ( 1- 1/3)
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by GMATGuruNY » Sun Oct 03, 2010 4:52 am
vongdn wrote:3^x - 3^(x-1) = 162, then x(x-1) = ?

How do I find x to solve the final question?
We could guess and check on this question and determine the correct answer quickly.

If x=4, then 3^4 = 81, which is too small, since the right side of the equation is 162.

Let's try x=5:

3^5 - 3^(5-1) = 162
3^5 - 3^4 = 162
3^4(3-1) = 162
81*2 = 162. This works.

So x(x-1) = 5*(5-1) = 5*4 = 20.
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by Rahul@gurome » Sun Oct 03, 2010 6:36 am
3^x - 3^(x-1) = 162 implies 3^x - (3^x)(3^-1) = 162
3^x [ 1 - (1/3)] = 162
(3^x)*(2/3) = 162
3^x = 81*3
3^x = 3^5
Since bases are the same, so exponents will also be equal.
Hence, x = 5.
x (x - 1) = 5*(5 - 1) = 20
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