Which of the following is the correct increasing order for a given number $α$ , $α > 0$ ?

$l o g_{2} α, l o g_{3} α, l o g_{e} α, l o g_{10} α$

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$l o g_{10} α, l o g_{3} α, l o g_{e} α, l o g_{2} α$

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$l o g_{10} α, l o g_{e} α, l o g_{2} α, l o g_{3} α$

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$l o g_{3} α, l o g_{e} α, l o g_{2} α, l o g_{10} α$

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Solution

The correct option is B
$l o g_{10} α, l o g_{3} α, l o g_{e} α, l o g_{2} α$

Since 10, 3, e, 2 are in decreasing order.
$l o g_{10} α, l o g_{3} α, l o g_{e} α, l o g_{2} α$ are in increasing order.

DIY- If there is $l o g_{\frac{1}{2}} α$ instead of $l o g_{2} α$ what will be the correct increasing order?

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