## How To Find Logarithm Of Any Number Using Log Table

## How To Find Logarithm Of Any Number Using Log Table

##### Log Table Explained

#### Log table explained with examples

There are many methods but we are going to use a convenient one.

Note: Here, we are going to find the log of some number with base 10.

Let’s find the **log of 5678.34**For convenience, The value of

**log 5678.34 = 3.7542**

3.7542 has two parts :

1) Characteristic

*(i.e. before decimal point which is 3)*

2) Mantissa

*(i.e. after decimal point which is 7542)*

Note :

*We use log table to find only Mantissa as characteristic can be found very easily by our self.*

We know that log (m×n) = log m + log n So, **5678.34 **can be written as **56.7834 × 10^2 **. So, **log 5678.34 = log 56.7834 + log 10^2**

Now **log 10^2 = 2** (log m^n = n log m).

Now here comes the main part i.e. log 56.7834

*Here are the steps –***1.** In the Log Table, look for the **row 56**. **2.** Then move to the right in the same row until you reach to **column 7** ( first digit after decimal point). **3.** It should have the value **7536** which should be written as **0.7536** *(as it is the decimal part)*. **4.** Now, in the same row, move to ** mean difference** table and note down the value under the

**column 8**( 56.7

**8**34) which should be 6.

**5.**Now add the mean difference to the value we obtained in column 7 ( i.e. 0.7536 + 0.0006 = 0.7542).

So we obtained the

**mantissa part i.e. 0.7542**.

**6.**Now characteristic of log 56.7834 is one less than the number of digits it has to the left of decimal point (i.e. 2–1=1)

**7.**Now, add characteristic and mantissa. ( 1 + 0.7542 = 1.7542)

To sum up the steps —

log 5678.34 = log 10^2 + log 56.7834

= 2 + 1.7542

=3.7542**So, we got log 5678.34 = 3.7542**

Lets consider another example : **log 1.35**

log 1.35 = log 10^-1 + log 13.5

= -1 + 1.1303

= 0.1303**So log 1.35 = 0.1303**

*Published on
September 18th, 2019 | by
Abhishek Mandal *