(2 log,05 + log,.42 + 3 log,.2) - 2 = m log,. 2. So find the value of 'm.
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Solution :
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We know the logarithmic laws :
i ) n log m = log mⁿ
ii ) log m + log n = log mn
iii ) log m - log n = log ( m/n )
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2log5 +log 3+3log2-1/2 log 36-2log10
= log5² + log 3 + log 2³- log√36-log10²
= log 25 + log3 + log 8 - log 6 - log 100
= log ( 25 × 3 × 8 ) - ( log 6 + log 100 )
= log 600 - log 600
= 0
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