compare-log-2-3-with-log-3-4-

Question Number 97390 by shaxzod last updated on 07/Jun/20

c o m p a r e {l o g}_{2} 3 w i t h {l o g}_{3} 4

Answered by mr W last updated on 07/Jun/20

9 > 8

3^{2} > 2^{3}

2 \log_{2} 3 > 3

\Rightarrow \log_{2} 3 > \frac{3}{2} = \frac{9}{6}

8 < 9

2^{3} = 4^{\frac{3}{2}} < 3^{2}

\frac{3}{2} \log_{3} 4 < 2

\Rightarrow \log_{3} 4 < \frac{4}{3} = \frac{8}{6} < \frac{9}{6} = \frac{3}{2} < \log_{2} 3

i . e . \log_{2} 3 > \log_{3} 4

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