[3.876] If log 2 = 0.3010 \:and \:log 3 = 0.4771,\: the\: value \:of \:\log

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TNPSC G4

10th CBSE Maths

If $log 2 = 0.3010 \:and \:log 3 = 0.4771,\: the\: value \:of \:\log_{5}{512} $is:

2.870

2.967

3.876

3.912

Explanation:

$\log_{5}{512}$=$\dfrac{log 512}{log 5}$
=$\dfrac{\log2^9}{\log(\dfrac{10}{2})}$
=$\dfrac{9 log 2}{log 10 -log 2}$
=$\dfrac{(9\times 0.3010}{1-0.3010}$
=$\dfrac{2.709}{0.699}$
=$\dfrac{2709}{699}$
=3.876

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