In numerical calculation, the** base of logarithm as 10**.this logarithm is **called common logarithm** or Briggesian logarithm in honor of Henry Briggs Finding common logarithm of any number: **(1)** Round off the number to** four significant number (2)** Find the** characteristic** of the logarithm of the number by inspection.**(3)** Find the **mantissa of the Logarithm** of the number from the** table.(4)** combine the two.

**Example:**

(i) Log 276.23

(ii) Log o.07058

**Solution:**

**(i)** 278.23 **round off** as 278.3

here** characteristic is 2** and the** mantissa,**

by using **Log table is 0.4443**

Therefore, **Log 278.23 = 2.4443**

**Example:Finding common logarithm of any number**

(ii) Log .07058

**Solution:**

**Characteristic** of the Log 0. 07058 is** -2** Which is written as** 2¯**.

By using **Log table,** the **mantissa is 0.8487 **so that

**Log 0.07058 = 2‾. 8487**

**common logarithm and natural logarithm:**

**Common logarithm** having **base 10**. Common logarithm also known as **decadic logarithm** after its** base 10**. We usually take** log x** this has mean **log ₁₀ x,** and this type of logarithm is more convenient to use in **numerical calculation**.** John Napier** prepared the logarithm table to the** base e**.** Napier logarithm** are also called natural logarithm. He released the first ever **log table in 1614**. log **ₑ** x conventionally given the Notation **ln x.**

**Value of e:**

e is an irrational number whose value is 2.7182818…..

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