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Question: \[- \frac{5}{16}\left( 1 + \frac{x}{2} + \left( \frac{x}{2} \right)^{2} + ..... \right)\]...

−516(1+x2+(x2)2+.....)- \frac{5}{16}\left( 1 + \frac{x}{2} + \left( \frac{x}{2} \right)^{2} + ..... \right)

A

1

B

–1

C

0

D

None of these

Answer

1

Explanation

Solution

a=log⁡27log⁡12=3log⁡3log⁡3+2log⁡2⇒log⁡3=2alog⁡23−aa = \frac{\log 27}{\log 12} = \frac{3\log 3}{\log 3 + 2\log 2} \Rightarrow \log 3 = \frac{2a\log 2}{3 - a}

= log⁡616=log⁡16log⁡6=4log⁡2log⁡2+log⁡3\log_{6}16 = \frac{\log 16}{\log 6} = \frac{4\log 2}{\log 2 + \log 3}= =4log⁡2log⁡2+2alog⁡23−a=4(3−a)3−a+2a=4.3−a3+a= \frac{4\log 2}{\log 2 + \frac{2a\log 2}{3 - a}} = \frac{4(3 - a)}{3 - a + 2a} = 4.\frac{3 - a}{3 + a}.