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

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

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New post 27 Nov 2017, 22:18
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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New post 27 Nov 2017, 23:51
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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New post 28 Nov 2017, 01:41
3^6x = 810,000;
3^3x = (810,000)^1/2 = 900

3^(3x-3)= (900/3^3) = 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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New post 28 Nov 2017, 03:44
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

Answer: 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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New post 28 Nov 2017, 05:04
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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 \(3^{3x}/27 = 900/27 = 100/3\)

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

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New post 29 Nov 2017, 17:13
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.

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

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New post 12 Jan 2018, 08:04
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
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Joined: 02 Sep 2009
Posts: 52285
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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New post 12 Jan 2018, 08:18
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...
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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New post 12 Jan 2018, 10:25
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
User avatar
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Joined: 02 Sep 2009
Posts: 52285
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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New post 12 Jan 2018, 10:31
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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 12 Jan 2018, 10:55
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.
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Joined: 02 Sep 2009
Posts: 52285
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

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New post 12 Jan 2018, 11:01
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.

Similar questions to practice:
https://gmatclub.com/forum/if-3-6x-8-10 ... 98777.html
https://gmatclub.com/forum/if-2-8x-6400 ... 34587.html

8. Exponents and Roots of Numbers



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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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