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

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

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

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

Or, $$2^{2a}*2^{2b} =2(2^9)$$

Or, $$2^{2a}*2^{2b} =2^{10}$$

Or, $$2^{2a + 2b} = 2^{10}$$

So, $$2a + 2b = 10$$

Or, $$a + b = 5$$, Answer must be (B)
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Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6048
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Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink]
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
$$4^a*4^b=2(8^3)$$

Or, $$2^{2a}*2^{2b}=2(2^9)$$

Or, $$2^{2a+2b}=2^{10}$$

Or, $$2a+2b=10$$

Or, $$a+b=5$$, Answer must be (B) 5
Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink]
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