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Math Expert V
Joined: 02 Sep 2009
Posts: 58335
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 79% (02:08) correct 21% (02:20) wrong based on 147 sessions

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If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

_________________
Senior Manager  G
Joined: 09 Aug 2017
Posts: 479
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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3^4*10^4= 3^6x
Take root of both side
900=3^3x...equ1

Now we have to solve for (3^(x-1))^3= (3^3x)/3^3 ....equ2
From equation 1 and 2, answer is 100/3.
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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3^6x = 810,000;
3^3x = (810,000)^1/2 = 900

3^(3x-3)= (900/3^3) = 100/3
Intern  B
Joined: 26 Sep 2017
Posts: 4
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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Given $$3^(6x) = 810,000$$
which is simplified as

$$(3^(3x))^2=9^2 * 10^4$$

$$3^(3x) = 9 * 10^2$$=$$3^2*10^2$$

hence, $$(3^(x-1))^3=((3^x)/3)^3=3^(3x)/3^3$$
=$$(3^2 * 10^2)/(3^3)$$
=100/3

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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3
Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

$$(3^{x−1})^3 = 3^{3x}/27$$

We know
$$3^{6x} = 810,000$$
So $$3^{3x} = 900$$ (taking square root on both sides)

We get $$3^{3x}/27 = 900/27 = 100/3$$

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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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1
Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

Let’s first re-express (3^(x - 1))^3, noting that when we have an exponent raised to an exponent, we multiply the two exponents. Thus, (3^(x - 1))^3 = 3^(3x - 3) = (3^3x)(3^-3) = (3^3x)/(3^3), so really we need to determine the value of 3^3x/27.

Simplifying the given equation, we have:

3^6x = 810,000

Taking the square root of both sides, we have:

3^3x = 900

Thus, (3^3x)/(27) = 900/27 = 100/3.

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Intern  B
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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1
gvrk_77 wrote:
Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

You are forgetting that x might not be an integer. So, $$3^{(6x)} = 810,000$$ for some irrational x, which is approximately 2.0639...
_________________
Intern  B
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

Bunuel wrote:
gvrk_77 wrote:
Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

You are forgetting that x might not be an integer. So, $$3^{(6x)} = 810,000$$ for some irrational x, which is approximately 2.0639...
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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1
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.
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Intern  B
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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I have no problem with the answer, my only problem is with the IF condition. I’m solving for what EXACT value of x wil be 3^6x= 81000.00

Bunuel wrote:
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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gvrk_77 wrote:
I have no problem with the answer, my only problem is with the IF condition. I’m solving for what EXACT value of x wil be 3^6x= 81000.00

Bunuel wrote:
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.

Not following you. Again, there exist some irrational x, for which $$3^{(6x)}$$ is EXACTLY 810,000. For that x, $$(3^{(x−1)})^3$$ is EXACTLY 100/3.

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_________________ If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   [#permalink] 12 Jan 2018, 12:01
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