Express in terms of 2 and 3 : 4.5 - Vidyadip

Question

Express in terms of $\log 2$ and $\log 3$ : $\log 4.5$

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Answer

$ \log 4.5$
$ =\log \frac{45}{10}$
$ =\log \frac{5 \times 3 \times 3}{5 \times 2}$
$ =\log \frac{3^2}{2}$
$ =\log 3^2-\log 2 \ldots . .\left[\log _{\mathrm{a}} \frac{m}{n}=\log _{\mathrm{a}} \mathrm{m}-\log _{\mathrm{a}} \mathrm{n}\right]$
$ =2 \log 3-\log 2 \ldots \ldots .\left[\log _{\mathrm{a}} \mathrm{m}^{\mathrm{n}}=\mathrm{n} \log _{\mathrm{a}} \mathrm{m}\right]$

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