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  4. The value of (0.2) log √5((1/4)+(1/8)+(1/16)+ ldots ∞) is equal to

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Q. The value of $(0.2)^{\log _{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty\right)}$ is equal to

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Solution:

$=0.2 \log _{\sqrt{5}}\left[\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \ldots \ldots . . \infty\right]={ }_{0.2} \log _{\sqrt{5}}\left[\frac{1 / 4}{1-1 / 2}\right]={ }_{(0.2)} \log _{\sqrt{5}}\left[\frac{1}{2}\right]={ }_5 \log _{\sqrt{5}} 2=2^2=4$