what is the benefits of using logarithms?

Answer 1

minimize your calculation process.

Answer 2

Before there were calculators people used logarithms to bring complicated operations down to a lower level.

Now however it's just that some phenomena are fairly well described by the logarithm function.

You can sometimes use logs to solve an equation with the unknown in the exponent: e.g.

1.3^(2n+1) = 7

Taking logs of both sides and using the exponent property of the log function gives
(2n + 1) log 1.3 = log 7

Divide log 7 by log 1.3, subtract 1, and divide by 2, and you have the value of n.

Also, if an experimenter believes that a quantity P is proportional to some power of w, but doesn't know what power, logs can be used to test this idea:

Measure values of P corresponding to many different values of w. Then plot P not against w, but log P against the logarithm of w. If these points lie fairly well on a straight line (allowing for experimental error), then drawing the line can give an equation in the form
log P = a + b*log w, where a and b can be found from the graph.

Then log P -a = b*log w
which can be written as
log(P/e^a) = log (w^b)

from which P/e^a = w^b and so
P = K w^b where K = e^a.

Thus the experimenter has found the power equation linking the two quantities.

Answer 3

by using logarithm,equations with powers of a number or a variable is converted into a simple equation waith addition and subtraction

Answer 4

If you're unsure of how many digits a certain number has, you can take the log of it (in base 10), round down, and that will tell you how many.

Answer 5

logs allow us to convert an exponential equation into an algebraic equation...
there aren't too many techniques for solving exponential, but many for algebraic ones..

Answer 6

They make long divisions and multiplications very easy.