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If 724 = (16)(6n), what is the value of n?

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sandy
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If 724 = (16)(6n), what is the value of n? [#permalink] New post   28 Oct 2018, 17:05
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If \(72^4 = (16)(6^n)\), what is the value of n?

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Re: If 724 = (16)(6n), what is the value of n? [#permalink] New post   29 Oct 2018, 09:20
sandy wrote:
If \(72^4 = (16)(6^n)\), what is the value of n?

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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? [#permalink] New post   30 Oct 2018, 19:07
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sandy wrote:
If \(72^4 = (16)(6^n)\), what is the value of n?

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\(72^4 = (16)(6^n)=4^26^n......6^n=\frac{72^4}{2^4}.....6^n=(\frac{72}{2})^4=36^4=6^{2*4}=6^8.......n=8\)

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Re: If 724 = (16)(6n), what is the value of n? [#permalink] New post   06 Aug 2024, 10:47
Hello from the GRE Prep Club BumpBot!

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Re: If 724 = (16)(6n), what is the value of n? [#permalink]
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