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Advanced Logarithms - Properties and Equations

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Which is the correct order for a given number $\alpha$ in increasing order.

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A
$\log _{2} \alpha, \log _{e} \alpha, \log _{3} \alpha, \log _{10} \alpha$
💡 Explanation:
We know that, greater the value of base lesser is the value of the logarithm

Also, $10<3<e(2.71)<2$

$\therefore $ For any positive number $\alpha $,

${ log } _{ 2 }\alpha >{ log } _{ e }\alpha >{ log } _{ 3 }\alpha >{ log } _{ 10 }\alpha $

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