why do we use log in calculation?

Answer 1

it can be used for big calculations including square roots and cube roots.The only catch is that it isn't that accurate

Answer 2

Logarithms (logs) make difficult calculations easier.

If you use logarithms, and anti-logs, via a table, for example, then:

- Muliplication and division become addition and subtraction. This is the foundation rule for the old slide rules, the way we did most math calculations before calculators came along

Example: What is 2.689 x 37.555?

Answer

= antilog [ log 2.689 + log 37.555 ]

= antilog [ 0.4295 + 1.5747 ] = antilog [ 2.0042 ]

= 100.97

(if you used a calculator to get the answer, it would be 100.985, so you see that using logarithms has an accuracy limitation)

- Exponents and roots become multiplication and division problems, again much easier, and do-able with a slide rule or paper and pencil.

For example, what is the fifth root of 97?

Answer:

= antilog [ (1/5) * (log 97) ] = antilog [ 0.2 * 1.987 ]

= antilog [ 0.3973 ]

= 2.497

So learning about logarithms gives you a way to understand the inner workings of calculations, and a quick way to do estimations of large numbers if you need to, especially if you don't have a calculator or computer handy.


Hope this helps!

Answer 3

To allow the transformation of an exponential equation into an easily solvable linear equation:

Compound interest calculations are the most common and perhaps the easiest to understand: If a bank says they pay you 5% compounded monthly, the monthly interest rate is .05/12 = .004166667. To calculate the balance after 5 years (60 months) you would use the equation Px(1.004166667)^60 where P is the original amount. That is a logrithmic (exponential) function. So with 2 keystrokes you could figure thay you'd have 1.283 times more than you started with.

The opposite problem is where logs are really helpful: Lets say you invested $10,000 and it grew to $26,580 in 12 years. What was your average annual return?

$26,580 = $10000 x (rate)^12

26580/10000 = rate^12
log (26580/10000) = 12 log(rate)
log (26500/10000) / 12 = log rate
.0352 = log rate
rate = 1.0846 so your average annual return was about 8.5%.

without the log function, these problems would be time consuming "guess and check" exercises.

Answer 4

Well, now days we don't, except in special situations.

The only places I normally use logs today are with pH in chemistry or with log graphs in plotting stock prices.

The reason why logs were so important 50 years ago is that they were necessary to do quick calculations using a slide rule, which is based on logs. Logs allow you to add exponents instead of multiply. Adding is a lot faster. With the advent of the hand calculator the main reason for using logs was eliminated.

But logs are a handy way of turning a exponent value into a simple number. As any number can be expressed as a power of another number (e and 10 are the most common bases).

By the way I still have my Post slide rule that I bought when I was in high school back in 1958.

Answer 5

The logarithm was invented to ease calculations at a time when calculators were not yet invented. They greatly simplified life by turning multiplication to addition and division to subtraction.

They are still used and studied now because of the interesting properties of the log function.

Answer 6

Logarithms were used to speed up calculations, when there were no calculators. However with the advent of calculators and computers this has become obsolete technology. However, logs are still used in statistics for logarithmic distribution curve.

Answer 7

My oldest brother was part of the generation that converted from pencil and paper to calculators. Before calculators and computers it was easiest in multiplication to convert numbers to the nearest three digits to a logarithmic scale and then add them together and convert back. (To divide you subtract.)

This method has gone the way of FORTRAN and slide rules. It is just obsolete because there is no need for it any more. A calculator that can do what my brother did with his first calculator can be purchased for the cost of a coffee and muffin from Starbucks.

Answer 8

we use log in calculation because it can be used for big calculations including square roots and cube roots.The only catch is that it isn't that accurate

Answer 9

we use logarithm in calculation so as to simplify it.using log u can convert tedious multiplication and division operations to simple addition or subtraction operations.

Answer 10

to avoid messy cube roots with x^(1/9) etc. you can do anything with logs. but the thing is it is not accurate(I will prefer caluclator to do any thing less than 9X10^99.