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30 Sep 2024, 09:44
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
85% (01:08) correct
14% (00:54) wrong based on 7 sessions
History
Date
Time
Result
Not Attempted Yet
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. \(2^{4(t-3)}\)
A. \(2^t\)
B. \(2^{t-3}\)
C. \(2^{3(t-3)}\)
D. \(2^{4t-3}\)
E. \(2^{4(t-3)}\)
10 Feb 2025, 10:06
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OE
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 \(2^3m = (2^4)^t,\) which is the same as \(2^3m = 2^{4t}\). 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.
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 \(2^3m = (2^4)^t,\) which is the same as \(2^3m = 2^{4t}\). 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.
