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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? [#permalink]

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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
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 01 Jul 2012, 19:04
Bunuel wrote:
ferrarih 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


Given: \(3^{6x}=(3^{3x})^2=90^2=8,100\) --> \(3^{3x}=90\).

\((3^{x-1})^3= 3^{3x-3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\).

Answer: D.


Hi Bunnel,

I know this is a silly doubt?

can we equate bases when powers are equal? i.e what you did in the above step?. I know that we equate powers when bases are equal, but i am not sure of equating bases when powers are equal.

Regards
Srinath
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 25 Aug 2014, 09:04
3^(6x)=8100=(3^4)(10^2)

Taking square roots,
3^(3x)=(3^2)(10)=90


[3^(x-1)]^3=3^(3x-3)
=3^3x/3^3 =90/(3x3x3)
=10/3

Answer D

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 26 Aug 2014, 00:25
\(3^{6x} = 8100\)

Square root both sides

\(3^{3x} = 90\)

Divide both sides by 27

\(\frac{3^{3x}}{27} = \frac{90}{27}\)

\(3^{3x-3} = \frac{10}{3}\)

\([3^{(x-1)}]^3 = \frac{10}{3}\)

Answer = D
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 22 Jul 2015, 21:12
Bunuel wrote:
ferrarih 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


Given: \(3^{6x}=(3^{3x})^2=90^2=8,100\) --> \(3^{3x}=90\).

\((3^{x-1})^3= 3^{3x-3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\).

Answer: D.


Can you tell me where I am going wrong with the following method:


\(3^{6x} = 8100\)

\(3^{6x}\)= \(3^{4}\) x \(2^{2}\) x \(5^{2}\)

6x=4
x=2/3

Substituting the value of x in \((3^{x-1})^3\), we get:

\((3^{2/3-1})^3\) = \((3^{-1})\)

= 1/9

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 23 Jul 2015, 01:08
3^3x=90

to find 3^3x-3 we can find multiplyer which is (3^3x)/3^3x-3=27

so, 90/27=10/3

D

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 23 Jul 2015, 01:56
8100 = 90^2

3^(6x) = 3^(3x)^2 = 90^2

3^(3x) = 90

3^(3x-3) = 3^(3x)/3^(3) = 90/27 = 10/3. Ans (D).
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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New post 29 Nov 2017, 01:29
Hello from the GMAT Club BumpBot!

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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?   [#permalink] 29 Nov 2017, 01:29
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