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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]  09 Sep 2016, 07:19
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42% (01:30) correct 57% (00:55) wrong based on 14 sessions
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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Question: 122
Page: 179
[Reveal] Spoiler: OA

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Last edited by Carcass on 04 Jan 2019, 10:41, edited 1 time in total.
Edited by Carcass
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Re: QOTD # 12 If t is an integer and 8m = 16 t , which of the fo [#permalink]  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]  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)

[Reveal] Spoiler:
D

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