If t is an integer and 8m = 16t, which of the following expresses m in terms of t ?

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问题 If t is an integer and 8m = 16^t, which of the following expresses m in terms of t ?

选项 A、2^t
B、2^t-3
C、2^3(t-3)
D、2^4t-3
E、2^4(t-3)

答案D

解析 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 2³m =(2⁴)^t, which is the same as 2³m = 2^4t. Solving for m and using the rules of exponents, you get m =

= 2^4t-3. The correct answer is Choice D.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship

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If t is an integer and 8m = 16t, which of the following expresses m in terms of t ?

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