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If 724 = (16)(6n), what is the value of n?
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28 Oct 2018, 17:05
28 Oct 2018, 17:05
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Question Stats:
82% (01:36) correct
17% (01:38) wrong based on 17 sessions
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Re: If 724 = (16)(6n), what is the value of n?
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29 Oct 2018, 09:20
29 Oct 2018, 09:20
sandy wrote:
Let's first rewrite both sides as powers of PRIME NUMBERS.
72 = (2)(2)(2)(3)(3) = (2³)(3²)
So, 74^4 = [(2³)(3²)]^4
= (2^12)(3^8)
6 = (2)(3)
So, 6^n = [(2)(3)]^n
= (2^n)(3^n)
16 = (2)(2)(2)(2) = 2^4
So, (16)(6^n) = (2^4)(2^n)(3^n)
= [2^(4+n)](3^n)
The given equation becomes: (2^12)(3^8) = [2^(4+n)](3^n)
We can see there that n must equal 8
Answer: 8
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Re: If 724 = (16)(6n), what is the value of n?
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30 Oct 2018, 19:07
30 Oct 2018, 19:07
Expert Reply
sandy wrote:
\(72^4 = (16)(6^n)=4^26^n......6^n=\frac{72^4}{2^4}.....6^n=(\frac{72}{2})^4=36^4=6^{2*4}=6^8.......n=8\)
Ans 8
