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Exponential Problem

by rintoo22 » Wed Mar 20, 2013 2:37 am
Q. If ((36 to the power x) = 8,100), what is the value of ((3x - 1)to the power of 3) ?

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

Please post the solution
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by Anju@Gurome » Wed Mar 20, 2013 2:48 am
rintoo22 wrote:Q. If ((36 to the power x) = 8,100), what is the value of ((3x - 1)to the power of 3)?
Are you sure that you have posted the question properly?
The solution for the question you have posted is beyond the scope of GMAT.

As far as I know, the actual question is as follows...
If 3^(6x) = 8100, what is the value of (3^(x - 1))^3?
3^(6x) = (3^(3x))^2 and 8100 = 90^2
So, 3^(3x) = 90 = 9*10 = (3^2)*10 = (3^3)*(10/3)
--> 3^(3x - 3) = 10/3
--> (3^(x - 1))^3 = 10/3

The correct answer is D.
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by rintoo22 » Wed Mar 20, 2013 3:12 am
Thanks Anju. You hit the nail on head. It was a typo. Thank for the Response. Much Appreciated
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by GMATGuruNY » Wed Mar 20, 2013 3:35 am
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The correct problem appears above.

3^6x = 8100
(3^3x)² = 8100
3^3x = 90.

(3^(x-1))^3
= 3^(3x-3)
= (3^3x)/3³
= 90/27 (substituting 3^3x = 90)
= 10/3.

The correct answer is D.
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by Brent@GMATPrepNow » Wed Mar 20, 2013 4:27 am
If 3^(6x) = 8100, what is the value of (3^(x - 1))^3?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9

Here's another approach

We're trying to find the value of 3^(x - 1))^3
Let's first simplify it by applying the Power of a Power law to get: 3^(3x - 3)
Then recognize that 3^(3x - 3) = (3^3x)/(3^3) [applying the Quotient Law in reverse]

We're told that 3^(6x) = 8100
Raise both sides by the power of 1/2 to get: 3^(6x)^(1/2) = 8100^(1/2)
Simplify to get: 3^(3x) = 90

Aside: raising a number to the power of 1/2 is the same as finding the square root of that number.

So, 3^(x - 1))^3 = 3^(3x - 3)
= (3^3x)/(3^3)
= 90/27
= [spoiler]3/10 = D[/spoiler]

Cheers,
Brent
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