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If log 2 = 0.3010 and log 3 = 0.4771, the value of log₅ 512 is:

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}

$\eqalign{ & {\log _5}512 \cr & = {{\log 512} \over {\log 5}} \cr & = {{\log {2^9}} \over {\log \left( {{{10} \over 2}} \right)}} \cr & = {{9\log 2} \over {\log 10 - \log 2}} \cr & = {{\left( {9 \times 0.3010} \right)} \over {1 - 0.3010}} \cr & = {{2.709} \over {0.699}} \cr & = {{2709} \over {699}} \cr & = 3.876 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@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}

$\eqalign{ & {\log _5}512 \cr & = {{\log 512} \over {\log 5}} \cr & = {{\log {2^9}} \over {\log \left( {{{10} \over 2}} \right)}} \cr & = {{9\log 2} \over {\log 10 - \log 2}} \cr & = {{\left( {9 \times 0.3010} \right)} \over {1 - 0.3010}} \cr & = {{2.709} \over {0.699}} \cr & = {{2709} \over {699}} \cr & = 3.876 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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