Iflog2=0.3010andlog3=0.4771,thevalueoflog5512=?Iflog⁡2=0.3010andlog⁡3=0.4771,thevalueoflog5512=?\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr} " /> Iflog2=0.3010andlog3=0.4771,thevalueoflog5512=?Iflog⁡2=0.3010andlog⁡3=0.4771,thevalueoflog5512=?\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr} " /> Iflog2=0.3010andlog3=0.4771,thevalueoflog5512=?Iflog⁡2=0.3010andlog⁡3=0.4771,thevalueoflog5512=?\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr} " />

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$\begin{aligned} If \log 2 = 0.3010 a n d \log 3 = 0.4771, \\ t h e v a l u e o f \log_{5} 512 = ? \end{aligned}$ $\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr}$

12.870
22.967
33.876
43.912

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \log_{5} 512 \\ = \frac{\log 512}{\log 5} \\ = \frac{\log 2^{9}}{\log (\frac{10}{2})} \\ = \frac{9 \log 2}{\log 10 - \log 2} \\ = \frac{(9 \times 0.3010)}{1 - 0.3010} \\ = \frac{2.709}{0.699} \\ = \frac{2709}{699} \\ = 3.876 \end{aligned}

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", "text": "

\begin{aligned} If \log 2 = 0.3010 a n d \log 3 = 0.4771, \\ t h e v a l u e o f \log_{5} 512 = ? \end{aligned}

$\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \log_{5} 512 \\ = \frac{\log 512}{\log 5} \\ = \frac{\log 2^{9}}{\log (\frac{10}{2})} \\ = \frac{9 \log 2}{\log 10 - \log 2} \\ = \frac{(9 \times 0.3010)}{1 - 0.3010} \\ = \frac{2.709}{0.699} \\ = \frac{2709}{699} \\ = 3.876 \end{aligned}

$\eqalign{ & {\log _5}512 \cr & = \frac{{\log 512}}{{\log 5}} \cr & = \frac{{\log {2^9}}}{{\log \left( {\frac{{10}}{2}} \right)}} \cr & = \frac{{9\log 2}}{{\log 10 - \log 2}} \cr & = \frac{{\left( {9 \times 0.3010} \right)}}{{1 - 0.3010}} \cr & = \frac{{2.709}}{{0.699}} \cr & = \frac{{2709}}{{699}} \cr & = 3.876 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: