How to find logarithms easilyHow to find the value of log2.7 by any shortcut or alternative methods?

Expert Answers
sciencesolve eNotes educator| Certified Educator

Notice that you may write 2.7=27/10, hence log 2.7 = log (27/10)

You need to remember the quotient property of logarithms, thus you should conver the logarithm log (27/10) in a difference of two logarithms such that:

log (27/10) = log 27 - log 10

You need to remember that log 10 = 1, hence log (27/10) = log 27 - 1

You may write 27 = 3^3 => log 27 = log 3^3 => log 27 = 3*log 3

You may use tables of common logarithms (base 10) for 1 to 10 to find log 3 = 0.477.

log 2.7 = 3*0.477 - 1 = 0.431

mlsiasebs eNotes educator| Certified Educator
It depends on the number you are taking the log of. If you have a number, such as 1 x 10^-3, then the log will be -3. If the number increases (ie 2 x 10^-3), the value of the log will increase to -2.7. Knowing this allows us to estimate the value to either make a reasonable estimate of the answer or to evaluate if an answer is in the appropriate range.
litteacher8 eNotes educator| Certified Educator
I am not sure if you are only looking for methods to calculate the logarithms by hand, but there are also several online calculators. Even if you are learning how to find logarithms by hand, you can use an online calculator to check your work. Here's one I found easily, but there are more. http://www.1728.org/logrithm.htm
jaiii07 | Student

...........(1)

Here 4 is called power or exponent or index and the number 2 is called the base.

.........(2)

Eqns (1) and (2) are equivalent. where Eqn (2) is stated as "log to the base 2 of 16 equals 4".

The power in eqn(1) becomes the value in eqn(2).

The base in eqn(1) becomes the base of log in eqn(2).

In general,

Logarithms having a base of 10 is called Common Logarithms and it is abbreviated as lg or log. The following values may be checked using "log" button on your calculator. lg 27.5=1.4393, lg 0.0204=-1.6903.

Logarithms having a base of e (where 'e' is a mathematical constant and it is approximately equals to 2.7183) is called Napierian or Natural or hyperbolic Logarithms and it is abbreviated as ln. The following values may be checked using "ln" button on your calculator. ln 3.65=1.2947, ln 0.182=-1.7037.

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To evaluate log 2.7 : (without using calculator)

==>  x = log 2.7

==> 10^x = 2.7

==> 10^x = 10^0.43 ...............(using log tables book)

from which, x = 0.43

therefore, log 2.7 = 0.43

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