Express the following as a single logarithm: 18 + 25 - 30 - Vidyadip

Question

Express the following as a single logarithm:$\log 18 + \log 25 - \log 30$

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Answer

$\log 18 + \log 25 - \log 30$
$= \log (2 x 3^2) + \log 5^2 - \log (2 \times 3 \times 5)$
$= \log 2 + \log 3^2 + 2 \log 5 - {\log 2 + \log 3 + \log 5}$
$= \log 2 + 2 \log 3 + 2 \log 5 - \log 2 - \log 3 - \log 5$
$= \log 3 + \log 5$
$= \log (3 \times 5)$
$= \log 15.$

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