Problem 0013 | Logarithm | bengalstudents.com

Bengalstudents ...Sun, 17/02/2013 - 9:40pm

উদাহরণ ১৩৷ প্রমান করো $\log 2 + 16\log \frac{{16}}{{15}} + 12\log \frac{{25}}{{24}} + 7\log \frac{{81}}{{80}} = 1$ [H.S ‘98]

প্রমান:

$\begin{array}{l} \log 2 + 16\log \frac{{16}}{{15}} + 12\log \frac{{25}}{{24}} + 7\log \frac{{81}}{{80}}\\ = \log 2 + 16\left( {\log 16 - \log 15} \right) + 12\left( {\log 25 - \log 24} \right) + 7\left( {\log 81 - \log 80} \right)\\ = \log 2 + 16\log {2^4} - 16\log \left( {3 \times 5} \right) + 12\log {5^2} - 12\log \left( {3 \times {2^3}} \right) + 7\log {3^4} - 7\log \left( {5 \times {2^4}} \right)\\ = \log 2 + 64\log 2 - 16\log 3 - 16\log 5 + 24\log 5 - 12\log 3 - 36\log 2 + 28\log 3 - 7\log 5 - 28\log 2\\ = 65\log 2 + \log 5 - 64\log 2\\ = \log 2 + \log 5\\ = \log 10\\ = 1\left( {proved} \right) \end{array}$

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Problem 0013 | Logarithm

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