Question

evaluate by using laws of logarithm

Answer 1

The answer is given below :

Now,

$log_{10}20 + log_{10}5 \\ \\ = \frac{ log_{e}20}{ log_{e}10 } + \frac{ log_{e}5 }{ log_{e}10} \\ \\ = \frac{ log_{e}20 + log_{e}5 }{ log_{e}10 } \\ \\ = \frac{ log_{e}(20 \times 5) }{ log_{e}10 } \\ \\ = \frac{ log_{e}100 }{ log_{e}10 } \\ \\ = \frac{ log_{e} {10}^{2} }{ log_{e}10} \\ \\ = \frac{2 \times log_{e}10 }{ log_{e}10 } \\ \\ = 2$

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