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13 May 2021, 02:45
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C
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Difficulty:
45%
(medium)
Question Stats:
63% (01:53) correct
37%
(02:19)
wrong
based on 160
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If \(m=9^{(x−1)}\), then in terms of m, \(3^{(4x−2)}\) must be which of the following?
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
16 May 2021, 06:30
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Bunuel
If \(m=9^{(x−1)}\), then in terms of m, \(3^{(4x−2)}\) must be which of the following?
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
\(3^{(4x-2)}= \)
\( = 3^{2(2x-1)}= \)
\( =9^{(2x-1)}=\)
Since \(9^{(2x-1)}=9*9^{(2x-2)}\) (check this: \(9*9^{(2x-2)}=9^{1+(2x-2)}=9^{(2x-1)}\)), then:
\( 9^{(2x-1)}=\)
\( =9*9^{(2x-2)}= \)
\( =9*(9^{(x-1)})^2= \)
Since \(m=9^{(x−1)}\)
\( 9*(9^{(x-1)})^2= \)
\( = 9m^2\).
Answer: C.
General Discussion
13 May 2021, 03:13
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Bunuel
If \(m=9^{(x−1)}\), then in terms of m, \(3^{(4x−2)}\) must be which of the following?
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9
\(m=9^{(x−1)}\)
CONCEPT: \((a^b)^c = a^{bc}\)
i.e. \(m=(3^2)^{(x−1)}\)
i.e. \(m=(3)^{(2x−2)}\)
\(3^{(4x−2)} = 3^{2(2x−1)} = (3^{(2x−1)})^2 = (3*3^{(2x−2)})^2 = (3*m)^2 = 9m^2 \)
Answer: Option C
