log-2-3-x-log-3-5-y-lg6-

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

{l o g}_{2} 3 = x, {l o g}_{3} 5 = y, l g 6 = ?

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

\log_{3} 5 = y \Rightarrow \log_{2} 5 = xy

\log 6 = \log (2 \times 3)

= \log 2 + \log 3

= \frac{1 + \log_{2} 3}{\log_{2} 10}

= \frac{1 + \log_{2} 3}{1 + \log_{2} 5}

= \frac{1 + x}{1 + xy}

Commented by mathdanisur last updated on 21/Jun/21

c o o l S i r t h a n k y o u

Answered by liberty last updated on 22/Jun/21

\log_{10} (6) = \log_{10} (2) + \log_{10} (3)

= \frac{1}{1 + \log_{2} (5)} + \frac{\log_{2} (3)}{1 + \log_{2} (5)}

= \frac{1 + x}{1 + xy} .

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