Which is the correct order for a given number | vedclass

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(B) We know that for a fixed number $\alpha > 1$,the value of $\log_{b}\alpha = \frac{\ln \alpha}{\ln b}$.Since $\ln \alpha$ is a positive constant,th

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$\log_{10}\alpha, \log_{3}\alpha, \log_{e}\alpha, \log_{2}\alpha$

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(B) We know that for a fixed number $\alpha > 1$,the value of $\log_{b}\alpha = \frac{\ln \alpha}{\ln b}$.Since $\ln \alpha$ is a positive constant,the value of $\log_{b}\alpha$ is inversely proportional to $\ln b$.Comparing the bases: $10 > 3 > e \approx 2.718 > 2$.Therefore,$\ln 10 > \ln 3 > \ln e > \ln 2$.Taking the reciprocal,we get $\frac{1}{\ln 10} Multiplying by $\ln \alpha$,we get $\log_{10}\alpha Thus,the correct increasing order is $\log_{10}\alpha, \log_{3}\alpha, \log_{e}\alpha, \log_{2}\alpha$.

Which is the correct order for a given number $\alpha > 1$ in increasing order?

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