COMEDK · Maths · 1. Basic of Mathematics
The value of \((0.2) \log _{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty\right)\) is
- A 4
- B \(\frac{1}{4}\)
- C 2
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\((0.2)\) \(=(0.2) \quad \log _{\sqrt{5}} \frac{1 / 4}{1-\frac{1}{2}}\) \(=(0.2)^{\log _{\sqrt{5}}\left(\frac{1}{2}\right)}\) \(=\left(\frac{1}{5}\right)^{\log _{\sqrt{5}}\left(\frac{1}{2}\right)}=\left(\frac{1}{2}\right)^{2 \log _{5} \frac{1}{5}}\)…
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