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Exponents help?

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Exponents help?

by doclkk » Fri Aug 07, 2009 10:20 am
If 3^6x = 8,100, what is the value of [3^x – 1]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

(D)

My thoughts:

[spoiler]I Simplifieid 3^6x = 27^3x. The other side, to 27^3-3

So 8100^-3 ?

Sorry - a little lost. [/spoiler]
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by real2008 » Fri Aug 07, 2009 10:36 am
r u sure that d is the answer? In fact i find no choice has the answer.
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Re: Exponents help?

by susamleesmith » Fri Aug 07, 2009 11:56 am
doclkk wrote:If 3^6x = 8,100, what is the value of [3^x – 1]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

(D)

My thoughts:

[spoiler]I Simplifieid 3^6x = 27^3x. The other side, to 27^3-3

So 8100^-3 ?

Sorry - a little lost. [/spoiler]
1.3^6x = 8,100 equals to (3^3x)^2=8100
2.Take the square root of both sides.Then you will have this (3^3x)=90
3.[3^x – 1]^3 equals to (3^3x) / 3^3
4.Instead of (3^3x) put 90 in the 3 line
5.You will have 90/27 .After simplification you will get D=10/3
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Re: Exponents help?

by doclkk » Fri Aug 07, 2009 1:11 pm
susamleesmith wrote:
doclkk wrote:If 3^6x = 8,100, what is the value of [3^x – 1]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

(D)

My thoughts:

[spoiler]I Simplifieid 3^6x = 27^3x. The other side, to 27^3-3

So 8100^-3 ?

Sorry - a little lost. [/spoiler]
1.3^6x = 8,100 equals to (3^3x)^2=8100
2.Take the square root of both sides.Then you will have this (3^3x)=90
3.[3^x – 1]^3 equals to (3^3x) / 3^3
4.Instead of (3^3x) put 90 in the 3 line
5.You will have 90/27 .After simplification you will get D=10/3
Very helpful

So its 90/27 because 3^-3 = 1/27 right
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by tom4lax » Sun Aug 09, 2009 7:47 am
Was there any shortcut that you used to calculate step 3?

3.[3^x – 1]^3 equals to (3^3x) / 3^3

Thanks
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by anand0408 » Sun Aug 09, 2009 8:23 am
3^[(x-1)^3]
= 3^[3x-3]
=3^3x/3^3 (since a^-b= 1/(a^b)

Hope that is clear enough
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Re: Exponents help?

by real2008 » Sun Aug 09, 2009 9:20 am
doclkk wrote:If 3^6x = 8,100, what is the value of [3^x – 1]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

(D)

My thoughts:

[spoiler]I Simplifieid 3^6x = 27^3x. The other side, to 27^3-3

So 8100^-3 ?

Sorry - a little lost. [/spoiler]

[3^x – 1]^3

is different from 3^[(x-1)^3].

People are requested to type properly and hence not to cause head crunching situation to others.
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