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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

Verified by Experts

Let ` log_(10) 3 gt 2/5`
` rArr 3 gt 10^(2/5)`
` rArr 3^(5) gt 10^(2)`, which is true
Now, ` log_(10) 3 lt 1/2`
` rArr 3 lt 10^(1/2)`
` rArr 3^(2) lt 10`, which is true
Hence, `2/5 lt log_(10) 3 lt 1/2`
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