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What is the value of n if
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23 Jan 2019, 16:09
23 Jan 2019, 16:09
Expert Reply
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Question Stats:
86% (01:12) correct
13% (01:05) wrong based on 146 sessions
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What is the value of n if \(4^{10} × 64^2 = 16^2 × 4^n\)?
A. 6
B. 10
C. 12
D. 15
E. 30
A. 6
B. 10
C. 12
D. 15
E. 30
Re: What is the value of n if
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27 Jan 2019, 08:36
27 Jan 2019, 08:36
2
Solution,
4 ^ 10 * 64 ^ 2 = 16 ^ 2 * 4 ^ n
or, 4 ^ 10 * 4 ^ 3*2 = 4 ^ 2 *2 * 4 ^ n
or, 4 ^ 10+6 = 4 ^ 4+n
or, 10 + 6 = 4 + n
or, n = 16 - 4
or, n = 12
Thus, the answer is C.
4 ^ 10 * 64 ^ 2 = 16 ^ 2 * 4 ^ n
or, 4 ^ 10 * 4 ^ 3*2 = 4 ^ 2 *2 * 4 ^ n
or, 4 ^ 10+6 = 4 ^ 4+n
or, 10 + 6 = 4 + n
or, n = 16 - 4
or, n = 12
Thus, the answer is C.
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Re: What is the value of n if
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27 Jan 2019, 10:22
27 Jan 2019, 10:22
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Carcass wrote:
What is the value of n if \(4^{10} × 64^2 = 16^2 × 4^n\)?
A. 6
B. 10
C. 12
D. 15
E. 30
A. 6
B. 10
C. 12
D. 15
E. 30
Let's rewrite all terms with 4 as the base
GIVEN: \(4^{10} × 64^2 = 16^2 × 4^n\)
Rewrite \(64\) and \(16\) as \(4^3\) and \(4^2\) to get: \(4^{10} × (4^3)^2 = (4^2)^2 × 4^n\)
Simplify by applying the Power of a Power law: \(4^{10} × 4^6 = 4^4 × 4^n\)
Simplify by applying the Product law: \(4^{16} = 4^{4+n}\)
This means: \(16 = 4+n\)
Solve: \(n = 12\)
Answer: C
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