Last visit was: 11 Jun 2024, 08:26 It is currently 11 Jun 2024, 08:26
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93669
Own Kudos [?]: 630880 [21]
Given Kudos: 82237
Send PM
CAT Tests Forum Quiz Mode
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   27 Nov 2017, 23:18
3
Kudos
18
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

74% (02:13) correct 26% (02:38) wrong based on 242 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
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
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14943
Own Kudos [?]: 65842 [6]
Given Kudos: 433
Location: Pune, India
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   28 Nov 2017, 06:04
1
Kudos
5
Bookmarks
Expert Reply
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)
General Discussion
User avatar
D
gvij2017
Director
Director
Joined: 09 Aug 2017
Posts: 687
Own Kudos [?]: 420 [0]
Given Kudos: 778
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   28 Nov 2017, 00:51
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.
"B"
User avatar
B
strawhat316
Intern
Intern
Joined: 15 Oct 2017
Posts: 11
Own Kudos [?]: 5 [0]
Given Kudos: 183
Location: India
Concentration: Marketing, Finance
Schools: IESE '20 (A) HEC Jan 2018 Intake (A)
GMAT 1: 710 Q49 V38
GPA: 3.09
WE:Engineering (Aerospace and Defense)
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   28 Nov 2017, 02:41
3^6x = 810,000;
3^3x = (810,000)^1/2 = 900

3^(3x-3)= (900/3^3) = 100/3
avatar
B
SachinDani
Intern
Intern
Joined: 26 Sep 2017
Posts: 4
Own Kudos [?]: 3 [0]
Given Kudos: 145
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   28 Nov 2017, 04:44
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
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18988
Own Kudos [?]: 22421 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   29 Nov 2017, 18:13
1
Kudos
Expert Reply
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
avatar
B
gvrk_77
Intern
Intern
Joined: 24 Oct 2016
Posts: 14
Own Kudos [?]: 1 [1]
Given Kudos: 3
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 09:04
1
Kudos
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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93669
Own Kudos [?]: 630880 [1]
Given Kudos: 82237
Send PM
CAT Tests Forum Quiz Mode
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 09:18
1
Kudos
Expert Reply
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...
avatar
B
gvrk_77
Intern
Intern
Joined: 24 Oct 2016
Posts: 14
Own Kudos [?]: 1 [0]
Given Kudos: 3
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 11:25
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...
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93669
Own Kudos [?]: 630880 [1]
Given Kudos: 82237
Send PM
CAT Tests Forum Quiz Mode
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 11:31
1
Kudos
Expert Reply
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.
avatar
B
gvrk_77
Intern
Intern
Joined: 24 Oct 2016
Posts: 14
Own Kudos [?]: 1 [0]
Given Kudos: 3
Send PM
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 11:55
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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93669
Own Kudos [?]: 630880 [0]
Given Kudos: 82237
Send PM
CAT Tests Forum Quiz Mode
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink] If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   12 Jan 2018, 12:01
Expert Reply
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



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
GMAT Club Bot
gmatclubot
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]
12 Jan 2018, 12:01
Moderator:
Bunuel
Math Expert
93669 posts