If 3^6x = 8,100, what is the value of [(3^x – 1)]^3 ?

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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

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)

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by Patrick_GMATFix » Mon May 24, 2010 11:29 am
question source plz

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by gmatcrasher2010 » Mon May 24, 2010 12:52 pm
Is this correct question? but I am not an expert, I might be wrong.

Need some expert guys advice.

I came across similar type of question while doing GMATPrep 1
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by clock60 » Mon May 24, 2010 1:01 pm
my shy attempt
3^(6x)=8100
3^(6x)=3^4*100
3^(6x-4)-10^2=0
3^(3x-2)*2-10^2=0
(3^(3x-2)-10)*(3^(3x-2)+10)=0 only 1st braket has sence
3^(3x-2)=10

[3^(x - 1)]^3 ? - think it must be 3^(x-1)*3=3^(3x-3)

3^(3x-2)=3^(3x-2+3-3)=3^(3x-3)+1=3^(3x-3)*3

3^(3x-3)*3=10

3^(3x-3)=10/3

so i got D
what is oa?

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by stephen@knewton » Mon May 24, 2010 1:08 pm
Crasher,

The key to your question from GMATprep is to recognize that because your variable appears within an exponent on base 2, you need to "create" a 3 somewhere on the left side of the equation. That way, you'll be able to cancel the 3s and compare the exponents of like bases.

You must also recognize the rule of exponents that (2^X)(2^Y) = 2^(X+Y) ... to help you remember that, recall that two squared times two squared is simply "two times two times two times two" or two to the fourth.

[apologies for spelling out the powers, y'all, I think it's often easier than using carrots to denote superscript].

Now ... with this problem, is there something you can factor out of the left side that will result in a 3 multiplied by a power of 2?? Answer follows as a spoiler, for anybody that wants to try it!
[spoiler]
If you factor 2^(X-2) out of the left side, you end up with [2^(X-2)](2^2 + 1) or 3[2^(X-2)]. The threes cancel, and that allows you to set the exponents equal. X-2 = 13 ... and you can take it from there![/spoiler]

Hope that helps! Steve
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by clock60 » Mon May 24, 2010 1:08 pm
gmatcrasher2010 wrote:Is this correct question? but I am not an expert, I might be wrong.

Need some expert guys advice.

I came across similar type of question while doing GMATPrep 1
Image
(2^x)-(2^x/4)=2^x*(1-1/4)=2^x*(3/4)=2^(x-2)*3

2^(x-2)*3=3*2^13, cancel 3, and left with

2^(x-2)=2^13
x-2=13
x=15

hope it helps

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by gmatcrasher2010 » Mon May 24, 2010 1:15 pm
Oops I creat confusion here.

Actually I was concerned about this thread's main post question.

3^6x = 8,100, what is the value of [(3^x - 1)]^3

How do we solve this problem from X, where we have 2 different base?

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by kevincanspain » Mon May 24, 2010 1:41 pm
mitzwillrockgmat 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

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)
We are given that 3^6x = 8100 and asked to find (3^(x-1))^3 = 3^(3x - 3)

Since 3^6x = 8100 , 3^3x = 90
3^(3x-3)= 90/3^3 =10/3
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by mitzwillrockgmat » Tue May 25, 2010 12:00 pm
Patrick_GMATFix wrote:question source plz
this question is part of a set of mock gmat exams prepared a gmat prep centre called, 'jamboree'. im not a student there & a friend passed it along. im putting up a image of the question to make it easier to read. :)

pls give your feedback on how to solve! thanks :)

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by mitzwillrockgmat » Tue May 25, 2010 12:07 pm
kevincanspain wrote:
mitzwillrockgmat 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

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)
Hello there! can you please elaborate here , how did u break down

3^6x = 8100 into 3^3x = 90

3^(3x-3)= 90/3^3 =10/3


thanks :)

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by jeffedwards » Tue May 25, 2010 7:10 pm
mitzwillrockgmat wrote: Hello there! can you please elaborate here , how did u break down

3^6x = 8100 into 3^3x = 90

3^(3x-3)= 90/3^3 =10/3


thanks :)

mitzwillrockgmat, hope this breakdown is understandable

3^6x = 8100
(3^3x)^2 = 8100 (pulled the 2 out of the left side to make visible)
(3^3x)^2 =90^2 (made the right side similar)
3^3x = 90 (we get this by taking the square root of both sides...to get rid of the squares)

Now we want to add the -3 in the exponent to make this equation the same as the question

(3^3x)(3^-3) = 90(3^-3) (multiply both sides by 3^-3)
3^(3x-3) = 90(3^-3) (combined on the left side; now we just need to simplify the right to get our answer)
90(3^-3)
90/27 (because 3^-3 is equal to 1/(3^3) or 1/27)
10/3 (simplified fraction by dividing both numbers by 9)

Hope that helps.

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by quantskillsgmat » Tue May 25, 2010 11:11 pm
to solve these type of problem always try to convert expression in given format then u can solve it very fast
here 3^6x=8100,so (3^3x)^2=8100
hence 3^3x=90
now we have to find (3^3x-1)^3=3^3x-3=3^3x/3^3=3^3x/27=90/27=10/3 ans
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