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Math Expert V
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If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

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

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

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

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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)

So, x=13

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

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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

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

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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

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Joined: 01 Mar 2015
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Re: If (5^13)(9^7)=3(15^x), what is the value of x?  [#permalink]

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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

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

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

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

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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?

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

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