GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Feb 2020, 20:03

### 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

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

# If (5^13)(9^7)=3(15^x), what is the value of x?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61302
If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

06 Jun 2016, 04:11
1
6
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:30) correct 20% (02:20) wrong based on 223 sessions

### HideShow timer Statistics

If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2450
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

06 Jun 2016, 04:52
(5^13)(9^7)=3(15^x)
=> 5^13 * 3^14 = 3 * 3^x * 5^x
=> 5^13 * 3^14 = 3^(x+1) * 5^x

Value of x = 13
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 518
GPA: 2.81
If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

06 Jun 2016, 05:40
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

(5^13)(9^7)=3(15^x)

or,(5^13)(3^14)=3(3^x)(5^x)

So, x=13

GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4331
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

06 Jun 2016, 08:42
1
Top Contributor
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

We can answer this question by keeping track of the 5's only.
Given: (5^13)(9^7)=3(15^x)
Rewrite as: (5^13)(9^7)=3(5^x)(3^x)
So, it must be true that (5^13) = (5^x)
So, x = 13

_________________
Test confidently with gmatprepnow.com
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4842
Location: India
GPA: 3.5
If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

06 Jun 2016, 09:55
1
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

$$(5^{13})$$$$(9^7)$$=$$3(15^x)$$

Or, $$(5^{13})$$$$(3^{14})$$=$$3(3^x)(5^x)$$

We do not need to go any further -

$$(5^{13})$$ = $$(5^x)$$

So, x = 13

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 01 Mar 2015
Posts: 67
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

23 Nov 2018, 12:52
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

For solving this type of questions, I always make prime factors

(5^13)(9^7)=3(15^x)

=>(5^13)(3^14)=3(3^x)(5^x)

=>3(5^13)(3^13)=3(3^x)(5^x)

Therefore, x=13

Posted from my mobile device
Intern
Joined: 15 Aug 2018
Posts: 49
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

12 Dec 2018, 06:01
GMATPrepNow wrote:
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

We can answer this question by keeping track of the 5's only.
Given: (5^13)(9^7)=3(15^x)
Rewrite as: (5^13)(9^7)=3(5^x)(3^x)
So, it must be true that (5^13) = (5^x)
So, x = 13

The step 15^x=(3^x)(5^x) confuses me. May you elaborate on the validity of that step?

Best, gota900
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4331
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

12 Dec 2018, 08:19
2
Top Contributor
gota900 wrote:
GMATPrepNow wrote:
Bunuel wrote:
If (5^13)(9^7)=3(15^x), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

We can answer this question by keeping track of the 5's only.
Given: (5^13)(9^7)=3(15^x)
Rewrite as: (5^13)(9^7)=3(5^x)(3^x)
So, it must be true that (5^13) = (5^x)
So, x = 13

The step 15^x=(3^x)(5^x) confuses me. May you elaborate on the validity of that step?

Best, gota900

I'm applying a useful exponent law that says (ab)^n = (a^n)(b^n)
So, 15^x = [(3)(5)]^x
= (3^x)(5^x)

Does that help?

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14100
Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

### Show Tags

07 Jan 2020, 07:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If (5^13)(9^7)=3(15^x), what is the value of x?   [#permalink] 07 Jan 2020, 07:21
Display posts from previous: Sort by