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If 4^a*4^b=2(8^3), what is the value of a+b?

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If 4^a*4^b=2(8^3), what is the value of a+b?  [#permalink]

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New post 21 Feb 2017, 04:29
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Re: If 4^a*4^b=2(8^3), what is the value of a+b?  [#permalink]

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New post 21 Feb 2017, 04:48
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Bunuel wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


Check answer explanation as mentioned below

Answer: option B
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Re: If 4^a*4^b=2(8^3), what is the value of a+b?  [#permalink]

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Bunuel wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


Let's rewrite all terms with the same base, and let's make 2 the common base.
Given: 4^a x 4^b = 2(8^3)
Rewrite 4 and 8 as powers of 2: (2^2)^a x (2^2)^b = 2((2^3)^3)
Simplify: 2^(2a) x 2^(2b) = (2)(2^9)
Simplify again: 2^(2a + 2b) = 2^10
Since the bases are now equal, we can conclude that 2a + 2b = 10
Divide both sides by 2 to get: a + b = 5

Answer: B

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Re: If 4^a*4^b=2(8^3), what is the value of a+b?  [#permalink]

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New post 23 Feb 2017, 09:39
Bunuel wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


The key to solving this problem is to obtain the same base for the expressions in the equation. We notice that 4 = 2^2 and that 8 = 2^3; thus, the common base will be 2. Let’s simplify the given expression:

(4^a)(4^b) = 2(8^3)

(2^2a)(2^2b) = 2(2^3)^3

2^(2a + 2b) = 2^1(2^9)

2^(2a + 2b) = 2^10

2a + 2b = 10

a + b = 5

Answer: B
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Re: If 4^a*4^b=2(8^3), what is the value of a+b?  [#permalink]

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