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If \(\log_{4}2 = a\) then \(\log_{2}2 \) is1. 1/2a2. 4a3. 1/a4. None of these |
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Answer» Correct Answer - Option 1 : 1/2a Concept: Logarithmic formula:
Where a ≠ 1, a > 0 and b ≠ 1, b > 0 and M, N are arbitrary positive numbers and p is any real number.
Calculation: Given: \(\log_{4}2 = a\) To find: \(\log_{2}2 \) Using property, \(\rm \log_{a}b = \frac{1}{\log_{b}a}\) \(\Rightarrow \log_{4}2 = \frac {1}{\log_{2}4}= \frac{1}{\log_{2}(2\times2)}\) Using property, loga M + loga N = loga (MN) \(\rm \Rightarrow a = \frac{1}{(\log_{2}2\ +\ log_{2}2)}\) \(\rm \Rightarrow a = \frac{1}{2\log_{2}2}\) \(\rm \Rightarrow 2\log_{2}2 = \frac{1}{a}\) \(\rm \therefore \log_{2}2 = \frac{1}{2a}\) |
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