# How do you calculate log 4270?

Nov 11, 2016

$\log 4270 = 3.6304$

#### Explanation:

$\log 4270$ means logarithm of $4270$ to base $10$.

Now we know that ${10}^{0} = 1$, $10 = {10}^{1}$, $100 = {10}^{2}$, $1000 = {10}^{3}$ and so on. Hence,

$\log 1 = 0$, $\log 10 = 2$, $\log 100 = 2$, $\log 1000 = 3$, $\log 10000 = 4$

As a number with one digit lies between $1$ and $10$, its log will be between $0$ and $1$

a number with two digits lies between $10$ and $100$, its log will be between $1$ and $2$

a number with three digits lies between $100$ and $1000$, its log will be between $2$ and $3$

a number with three digits lies between $1000$ and $10000$, its log will be between $3$ and $4$

and as $4270$ lies between $1000$ and $10000$, it will be more than $3$ but less than $4$.

Here $3$ i.e. number to the left of decimal "the whole number"part is called characteristic and is decided by number of digits in the given number. In fact, it is one less than number of digits.

But $\log 4270$ will be $3. - - - -$, and latter portion is called mantissa , the positive fractional part of logarithm. This number is available from logarithmic tables.

For $4270$ it is $6304$ and hence

$\log 4270 = 3.6304$

Note that for $427$ it will be $2.6304$