How to calculate 3 × 7 by using logarithm?This is a story about Newton I...

aanpalendmw

aanpalendmw

Answered

2022-07-17

How to calculate 3 × 7 by using logarithm?
This is a story about Newton I read once when I was a child. Now that book is lost and I can only tell you what I remember.
When Newton was young, he had been already famous in curiosity and smart. His family hired a helper. One day, she asked him to go to the market with her because she wasn't good at math. At the market, there was a problem that needed to calculate 3 × 7. So the helper asked Newton. After a quick thinking using logarithm, he got the result that 3 × 7 must larger than 20 and smaller than 22...
So, my question is how did he do that calculate? How to use logarithm to get the result 20 < 3 × 7 < 22? Thank you so much.
The story countinues:
... and about to say the result. Before he could finish his math, a near by person had been listened to the conversation and jumped in: "3 times 7 is 21". "Wow, you are smarter than my Newton", said by the helper. "Indeed, you are smarter than Newton", Newton laughed away.

Answer & Explanation

cindysnifflesuz

cindysnifflesuz

Expert

2022-07-18Added 19 answers

This story is very unlikely to be true, but anyway...
log ( 3 × 7 ) = log ( 3 ) + log ( 7 )
Assuming we're using base-10 logarithms and that Newton has memorized some base-10 logs to two decimal places:
0.47 < log ( 3 ) < 0.48 0.84 < log ( 7 ) < 0.85 1.31 < log ( 3 ) + log ( 7 ) < 1.33
Since log ( 20 ) < 1.31 and log ( 22 ) > 1.34, that gives you the answer.

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