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If 4^a*4^b=2(8^3), what is the value of a+b?
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21 Feb 2021, 10:51
21 Feb 2021, 10:51
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 4
B. 5
C. 6
D. 7
E. 8
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
If 4^a*4^b=2(8^3), what is the value of a+b?
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21 Feb 2021, 11:14
21 Feb 2021, 11:14
Solution:
\(4^a*4^b=2^2^a*2^2^b\)
\(2(8^3)=2(2^3^*^3)=2(2^9)=2^1^0\)
\(2^2^a*2^2^b=2^1^0\)
2a+2b=10
Dividing throughout by 2
a+b=5
IMO B
Hope this helps!
\(4^a*4^b=2^2^a*2^2^b\)
\(2(8^3)=2(2^3^*^3)=2(2^9)=2^1^0\)
\(2^2^a*2^2^b=2^1^0\)
2a+2b=10
Dividing throughout by 2
a+b=5
IMO B
Hope this helps!
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If 4^a*4^b=2(8^3), what is the value of a+b?
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21 Feb 2021, 11:50
21 Feb 2021, 11:50
Carcass 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
A. 4
B. 5
C. 6
D. 7
E. 8
\(4^a*4^b = 2*(8^3)\)
\(2^{2a}*2^{2b} = 2*(2^3)^3\)
\(2^{2a+2b} = 2^{10}\)
When the bases are equal, the powers are equal
\(2a + 2b = 10\)
\(a + b = 5\)
Hence, option B
