Iflog2=0.30103,thenumberofdigitsin450is−Iflog⁡2=0.30103,thenumberofdigitsin450is−\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr} " /> Iflog2=0.30103,thenumberofdigitsin450is−Iflog⁡2=0.30103,thenumberofdigitsin450is−\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr} " /> Iflog2=0.30103,thenumberofdigitsin450is−Iflog⁡2=0.30103,thenumberofdigitsin450is−\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr} " />

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$\begin{aligned} If \log 2 = 0.30103, \\ the number of digits in 4^{50} is - \end{aligned}$ $\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr}$

130
231
3100
4200

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \log 4^{0} \\ = 50 \log 4 \\ = 50 \log 2^{2} \\ = (50 \times 2) \log 2 \\ = 100 \times \log 2 \\ = (100 \times 0.30103) \\ = 30.103 \\ ∴ characteristic = 30, \\ Hence, the number of digits in 4^{50} = 31 \end{aligned}

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", "text": "

\begin{aligned} If \log 2 = 0.30103, \\ the number of digits in 4^{50} is - \end{aligned}

$\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \log 4^{0} \\ = 50 \log 4 \\ = 50 \log 2^{2} \\ = (50 \times 2) \log 2 \\ = 100 \times \log 2 \\ = (100 \times 0.30103) \\ = 30.103 \\ ∴ characteristic = 30, \\ Hence, the number of digits in 4^{50} = 31 \end{aligned}

$\eqalign{ & \log {4^0} \cr & = 50\log 4 \cr & = 50\log {2^2} \cr & = \left( {50 \times 2} \right)\log 2 \cr & = 100 \times \log 2 \cr & = \left( {100 \times 0.30103} \right) \cr & = 30.103 \cr & \therefore {\text{characteristic}} = 30, \cr & {\text{Hence, the number of digits in }}{{\text{4}}^{50}} = 31 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: