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The value of log10 \(\sqrt{10\sqrt{10\sqrt{10\sqrt{10}}}}\)......... to ∞ is 

(a) 4 

(b) 3 

(c) 2 

(d) 1

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(d) 1

Given exp. = log10 \(\bigg(10^{\frac{1}{2}}\,10^{\frac{1}{4}}\,10^\frac{1}{8}...... to\,∞\bigg)\)

= log10 \(10^{\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......to\,∞\big)}\)

\({\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......to\,∞\big)}\). log10 10    [Using loga xn = n loga x]

\(\frac{\frac{1}{2}}{\big(1-\frac{1}{2}\big)}\) x 1 = 1

\(\big(\) Using sum of GP of infinite terms = \(\frac{a}{1-r}\big)\)

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