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Prove that 2/5 lt log(10) 3 lt 1/2....

Prove that `2/5 lt log_(10) 3 lt 1/2`.

Text Solution

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`x= log_(20) 3`
` rArr 1/x = log_(3) 20`
We know that ` 3^(2) lt 20 lt 3^(3)`
` rArr 2 lt log_(3) 20 lt 3`
` rArr 2 lt 1/x lt 3`
` rArr x in (1/3,1/2)`
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