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If 2^13*9^7=3(6^k), what is the value of k?
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04 Sep 2021, 05:41
04 Sep 2021, 05:41
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If \(2^{13}*9^7=3(6^k)\), what is the value of k?
(A) 7
(B) 13
(C) 14
(D) 15
(E) 20
(A) 7
(B) 13
(C) 14
(D) 15
(E) 20
Re: If 2^13*9^7=3(6^k), what is the value of k?
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04 Sep 2021, 07:28
04 Sep 2021, 07:28
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\(2^{13}*9^7=3(6^k)\)
\(2^{13}*3^{2*7} = 3 * 3^k * 2^k\)
\(2^{13}*3^{2*7} = 3^{k+1} * 2^k\)
We can compare the power of either \(2\) or \(3\)
\(k = 13\)
Answer B
\(2^{13}*3^{2*7} = 3 * 3^k * 2^k\)
\(2^{13}*3^{2*7} = 3^{k+1} * 2^k\)
We can compare the power of either \(2\) or \(3\)
\(k = 13\)
Answer B
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If 2^13*9^7=3(6^k), what is the value of k?
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04 Sep 2021, 08:37
04 Sep 2021, 08:37
1
\(2^{13}*9^7=3(6^k)\)
Rearranging left and right hand side we get
\(2^{13}*3^{2*7}=3((2*3)^k)\) = \(2^{13}*3^14=3*3^k * 2^k\) = \(3^{k+1} * 2^k\)
We can compare powers of 2 or 3 on both the sides. Doing both just to show how it is done
Comparing power of 2 we get: 13 = k
Comparing power of 3 we get: 14 = k+1 => k = 13
So, Answer will be B
Hope it helps!
Rearranging left and right hand side we get
\(2^{13}*3^{2*7}=3((2*3)^k)\) = \(2^{13}*3^14=3*3^k * 2^k\) = \(3^{k+1} * 2^k\)
We can compare powers of 2 or 3 on both the sides. Doing both just to show how it is done
Comparing power of 2 we get: 13 = k
Comparing power of 3 we get: 14 = k+1 => k = 13
So, Answer will be B
Hope it helps!
