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Wed Nov 25, 2020 6:38 am
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C
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Difficulty:
35%
(medium)
Question Stats:
69% (01:57) correct
31%
(02:15)
wrong
based on 195
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If \(2^{a + 2} - 2^{a – 2} = 15* 4^b,\) what is \(b\) in terms of \(a\) ?
A. \(\frac{a}{4}\)
B. \(\frac{a}{2}\)
C. \(\frac{a}{2} -1\)
D. \(a - 2\)
E. \(a - 1\)
A. \(\frac{a}{4}\)
B. \(\frac{a}{2}\)
C. \(\frac{a}{2} -1\)
D. \(a - 2\)
E. \(a - 1\)
Wed Nov 25, 2020 6:42 am
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sjuniv32
\(2^{a + 2} - 2^{a – 2} = 15* 4^b\);
Factor out \(2^{a-2}\):
\(2^{a - 2}(2^4 - 1) = 15* 4^b\);
\(2^{a - 2}*15 = 15* 4^b\);
\(2^{a - 2} = 4^b\);
\(2^{a - 2} = 2^{2b}\);
\(a - 2 = 2b\);
\(b = \frac{a}{2} - 1\).
Answer: C.
Wed Nov 25, 2020 10:43 pm
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If \(2^{a + 2} - 2^{a – 2} = 15* 4^b,\) what is \(b\) in terms of \(a\) ?
\(4*2^a - 2^a/4 = 15*2^{2b}\)
\(\frac{15*2^a}{4} = 15*2^{2b}\)
\(2^a = 2^{2b+2}\)
a = 2b+2
\(b = \frac{a-2}{2} = \frac{a}{2} - 1\)
IMO C
\(4*2^a - 2^a/4 = 15*2^{2b}\)
\(\frac{15*2^a}{4} = 15*2^{2b}\)
\(2^a = 2^{2b+2}\)
a = 2b+2
\(b = \frac{a-2}{2} = \frac{a}{2} - 1\)
IMO C
