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Question: If a = log<sub>3</sub>log<sub>3</sub>2. An integer r satisfying 1 \<\(2^{( - r + 3^{- a})}\)\< 2 mus...

If a = log3log32. An integer r satisfying 1 <2(−r+3−a)2^{( - r + 3^{- a})}< 2 must be less than

A

–1

B

0

C

1

D

2

Answer

2

Explanation

Solution

1<2(−r+3−a)1 < 2^{( - r + 3^{- a})} < 2

a = log3 log3 2 ⇓\Downarrow0 < – r + 3–a < 1

3a = log32 ̃ 3–a = log23

log2 3 – r > 0

̃ log2 3 > r, log2 3 < 1 + r

1 < log2 3 < 2

̃ r = 1