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

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Bunuel
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If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   06 Jun 2016, 05:11
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If \((5^{13})(9^7)=3(15^x)\), what is the value of x?

(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
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D
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BrentGMATPrepNow
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   06 Jun 2016, 09:42
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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

Answer:
Show Spoiler
D
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   06 Jun 2016, 05:52
(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
Answer D
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   06 Jun 2016, 06:40
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

Correct answer D
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   06 Jun 2016, 10:55
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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

Answer must be (D) 13
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   23 Nov 2018, 13:52
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

Answer Choice (D)

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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   12 Dec 2018, 07:01
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

Answer:
Show Spoiler
D


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

Best, gota900
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BrentGMATPrepNow
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If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   Updated on: 25 Apr 2021, 13:03
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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

Answer:
Show Spoiler
D


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?

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Originally posted by BrentGMATPrepNow on 12 Dec 2018, 09:19.
Last edited by BrentGMATPrepNow on 25 Apr 2021, 13:03, edited 1 time in total.
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   18 Apr 2021, 01:00
BrentGMATPrepNow 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

Answer:
Show Spoiler
D


How can you be certain that it must be true that (5^13) = (5^x) ?
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink] New post   11 Sep 2022, 16:59
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Re: If (5^13)(9^7) = 3(15^x), what is the value of x? [#permalink]
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