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If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
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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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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^(x1))^3= (3^3x)/3^3 ....equ2 From equation 1 and 2, answer is 100/3. "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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28 Nov 2017, 01:41
3^6x = 810,000; 3^3x = (810,000)^1/2 = 900
3^(3x3)= (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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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, \((3^(x1))^3=((3^x)/3)^3=3^(3x)/3^3\) =\((3^2 * 10^2)/(3^3)\) =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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28 Nov 2017, 05:04
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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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29 Nov 2017, 17:13
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 reexpress (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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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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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
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12 Jan 2018, 08:18
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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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...



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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
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12 Jan 2018, 10:31
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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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
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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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If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
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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/if36x810 ... 98777.htmlhttps://gmatclub.com/forum/if28x6400 ... 34587.html8. Exponents and Roots of Numbers Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
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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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If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?
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