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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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01 Jul 2012, 15:44
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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
[Reveal] Spoiler: OA

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

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01 Jul 2012, 15:50
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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.
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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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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25 Aug 2014, 08:37
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Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3? [#permalink]

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

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