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Question Number 144120 by mathdanisur last updated on 21/Jun/21

$${log}_{2}3=x,{log}_{3}5=y,lg6=?$$

Answered by Ar Brandon last updated on 21/Jun/21

$${\log }_{3}5=\mathrm{y}\Rightarrow {\log }_{2}5=\mathrm{xy}$$$$\log 6=\log \left(2\times 3\right)$$$$=\log 2+\log 3$$$$=\frac{1+{\log }_{2}3}{{\log }_{2}10}$$$$=\frac{1+{\log }_{2}3}{1+{\log }_{2}5}$$$$=\frac{1+\mathrm{x}}{1+\mathrm{xy}}$$

Commented by mathdanisur last updated on 21/Jun/21

$$coolSirthankyou$$

Answered by liberty last updated on 22/Jun/21

$$\log {}_{10}\left(6\right)=\log {}_{10}\left(2\right)+\log {}_{10}\left(3\right)$$$$=\frac{1}{1+\log {}_2\left(5\right)}+\frac{\log {}_2\left(3\right)}{1+\log {}_2\left(5\right)}$$$$=\frac{1+\mathrm{x}}{1+\mathrm{xy}}.$$

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