Question 1147150: Problem with solution / explanation:
Multiply 23.14 by 5.062 using logarithms.
log 23.14 = 1.364368 **
log 5.062 = 0.704322 **
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2.068685
product; 117.1347
** My questions:
How was the numbers obtained from the table?
How was product obtained from adding the logs?
Non-homework.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The log of 23 is the log of 2.3 from the table, and the 1 in front of that log comes from the fact that 23 is 10^1.something.
The log of 117, without looking at the table, is 2 something, because 10^2=100
You add the logs because to multiply one log by another, it is the addition of both actual logs.
multiplying a log by a number is the same as the log^to that number.
Nowadays, people can get the log from a calculator, but in the old days, we used log tables to do it and then took anti-logs at the end to get the number back. It is how we multiplied very large numbers, or numbers with decimal points, which are basically the same thing in log world.
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