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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
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25 Jan 2021, 05:34
25 Jan 2021, 05:34
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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
Kudos for the right answer and explanation
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If (5^13)(9^7)=3(15^x), what is the value of x? (A) 7 (B) 9 (C) 11 (D
[#permalink]
25 Jan 2021, 06:34
25 Jan 2021, 06:34
Carcass 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
Kudos for the right answer and explanation
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Kudos for the right answer and explanation
APPROACH #1: Keep 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: D
APPROACH #2: Keep track of all values
Given: (5^13)(9^7)=3(15^x)
Rewrite 9 as 3^2 and rewrite 15^x as (3^x)(5^x) to get: (5^13)(3^2)^7=3(5^x)(3^x)
Simplify: (5^13)(3^14)=3(5^x)(3^x)
Since 3(3^x) = 3^(x+1), we get: (5^13)(3^14)=(5^x)(3^x+1)
At this point, we can use the fact that 5^13 = 5^x OR the fact that 3^14 = 3^(x+1)
If we use 5^13 = 5^x, then it must be the case that x = 13
If we use 3^14 = 3^(x+1), then we reach the same conclusion that x = 13
Answer: D
gmatclubot
If (5^13)(9^7)=3(15^x), what is the value of x? (A) 7 (B) 9 (C) 11 (D [#permalink]
25 Jan 2021, 06:34
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