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QOTD # 12 If t is an integer and 8m = 16 t , which of the fo

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QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink] New post 09 Sep 2016, 07:19
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If t is an integer and \(8m = 16^t\) , which of the following expresses m in terms of t ?

a. \(2^t\)

b. \(2^{t-3}\)

c. \(2^{3(t-3)}\)

d. \(2^{(4t-3)}\)

e. \(2^{4(t-3)\)

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[Reveal] Spoiler: OA

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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink] New post 09 Sep 2016, 07:27
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Explanation

Note that all of the choices are expressions of the form 2 raised to a power. Expressing 8 and 16 as powers of 2, you can rewrite the given equation \(8m = 16^t\) as \(2^3\) m = \(2^4t\) .Solving for \(m\) and using the rules of exponents, you get

\(m=\frac{2^{4t}}{2^3}=2^{4t-3}\)

The correct answer is Choice D.
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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink] New post 09 Sep 2016, 14:01
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Carcass wrote:
If t is an integer and \(8m = 16^t\) , which of the following expresses m in terms of t ?

  • \(2^t\)
  • 2^(t–3)
  • 2^3(t–3)
  • 2^4(t–3)
  • 2^4(t–3)


Given: 8m = 16^t [solve for m]
Divide both sides by 8: m = [16^t]/8

Rewrite numerator and denominator as powers of 2
16^t = (2⁴)^t = 2^(4t)
8 = 2^3

So, we get: m = [2^(4t)]/[2^3]
Apply Quotient rule to get: m = 2^(4t - 3)

Answer:
[Reveal] Spoiler:
D


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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink] New post 24 May 2017, 22:53
Can someone explain why the answer is not Choice A, 2^t? It seems that the most direct way to simplify the equation and have m defined in terms of t is to divide by 8. 8m=16^t, so m=2^t. Why is this answer incorrect?
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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink] New post 25 May 2017, 00:31
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Here \(8m=16^t\) or \(m=\frac{16^t}{8}\) but this is not equal to \(2t\).

Say \(t=2\) and \(m=\frac{16^2}{8}=\frac{256}{8}=32\).

So if \(m=2t\) should be \(m = 2 \times 2 = 4\).


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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo   [#permalink] 25 May 2017, 00:31
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