Question
Express the following as a single logarithm:$\frac{1}{2} \log 25-2 \log 3+\log 36$
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Answer
$\frac{1}{2} \log 25-2 \log 3+\log 36 $
$ =\frac{1}{2} \log 5^2-2 \log 3+\log \left(2^2 \times 3^2\right) $
$ =\frac{1}{2} \times 2 \log 5-2 \log 3+\log 2^2+\log 3^2$
$ =\log 5+2 \log 2 $
$ =\log 5+\log 2^2 $
$ =\log 5+\log 4$
$=\log (5 \times 4) $
$ =\log 20 .$
$ =\frac{1}{2} \log 5^2-2 \log 3+\log \left(2^2 \times 3^2\right) $
$ =\frac{1}{2} \times 2 \log 5-2 \log 3+\log 2^2+\log 3^2$
$ =\log 5+2 \log 2 $
$ =\log 5+\log 2^2 $
$ =\log 5+\log 4$
$=\log (5 \times 4) $
$ =\log 20 .$
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