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If 2^a8^b=64
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03 Mar 2021, 02:14
03 Mar 2021, 02:14
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If \(2^a8^b=64\) and \(9^a3^b=27\), then what is the value of a??
A. 1/2
B. 3/5
C. 2/3
D. 1
E. 3/2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 1/2
B. 3/5
C. 2/3
D. 1
E. 3/2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: If 2^a8^b=64
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03 Mar 2021, 03:52
03 Mar 2021, 03:52
1
Carcass wrote:
If \(2^a8^b=64\) and \(9^a3^b=27\), then what is the value of a??
A. 1/2
B. 3/5
C. 2/3
D. 1
E. 3/2
A. 1/2
B. 3/5
C. 2/3
D. 1
E. 3/2
\(2^a8^b=64\)
\(2^a2^{3b}=2^6\)
\(2^{a+3b}=2^6\)
\(a + 3b = 6\) .......... (1)
\(9^a3^b=27\)
\(3^{2a}3^b=3^3\)
\(3^{2a+b}=3^3\)
\(2a + b = 3\) ........ (2)
Multiply (2) by 3 and subtract (1) from it;
\(6a + 3b = 9\)
\(a + 3b = 6\)
\(5a = 3\)
\(a = \frac{3}{5}\)
Hence, option B
gmatclubot
Re: If 2^a8^b=64 [#permalink]
03 Mar 2021, 03:52
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