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Q.

$\log_{5} \sqrt{5} + \log_{10} \sin 90 ° + 9^{\log_{9} 2^{- 1}} + \log_{9} \sqrt{3 \sqrt{3}} =$

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a

1

b

\frac{3}{4}

c

\frac{7}{4}

d

\frac{11}{8}

answer is B.

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Detailed Solution

\log_{5} \sqrt{5} + \log_{10} \sin 90 ° + 9^{\log_{9} 2^{- 1}} + \log_{9} \sqrt{3 \sqrt{3}} =

$\Rightarrow \log_{5} 5^{\frac{1}{2}} + \log_{10}^{1} + 9^{\log 9^{\frac{1}{2}}} + \log_{9} 3^{\frac{3}{4}}$

$\Rightarrow \frac{1}{2} \log_{5} 5 + 0 + \frac{1}{2} + \frac{3}{4} \times \frac{1}{2} \log_{3} 3$

$\Rightarrow \frac{1}{2} + \frac{1}{2} + \frac{3}{8} \Rightarrow \frac{11}{8}$

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