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

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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**

...........(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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