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Question
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Solution
We have to show that, `2/5 < log_10 3 < 1/2`
i.e., to show that,
`2/5 < log_10 3` and `log_10 3 < 1/2`
i.e., to show that,
2 < 5log103 and 2 log103 < 1
i.e., to show that,
2 log1010 < 5 log103 and 2 log103 < log1010 ...[∵ log1010 = 1]
i.e., to show that,
log10102 < log1035 and log1032 < log1010
i.e., to show that,
102 < 35 and 32 < 10
i.e., to show that,
100 < 243 and 9 < 10
which is true
∴ `2/5 < log_10 3 < 1/2`.
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