If $a = 1, b = {log}_{e} 2, c = {log}_{e} 3$ , then which condition is true?

a < b < c

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a > b > c

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a < c < b

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b < a < c

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Solution

The correct option is C $b < a < c$
$a = 1$
$b = l n 2$
$c = l n 3$
Now we know that
$2 < e < 3$
Hence
$0 < l n 2 < 1$
while $1 < l n 3$
since $l n e = 1$
Hence
$b < a < c$

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