# Logarithms Questions

**FACTS AND FORMULAE FOR LOGARITHMS QUESTIONS**

**EXPONENTIAL FUNCTION**

** **For every

or

Here is called as exponential function and it is a finite number for every .

**LOGARITHM**

Let a,b be positive real numbers then can be written as

e.g,

**(i) Natural Logarithm :*** * is called Natural logarithm or Naperian Logarithm, denoted by ln N i.e, when the base is 'e' then it is called as Natural logarithm.

e.g ,

**(ii) Common Logarithm :*** *is called common logarithm or Brigg's Logarithm i.e., when base of log is 10, then it is called as common logarithm.

e.g

,

**PROPERTIES OF LOGARITHM**

**1. **

**2. **

**3. **

**4. **

**5. **

**6. **

**7. **

**CHARACTERISTICS AND MANTISSA**

**Characteristic : **The integral part of logarithm is known as characteristic.

**Mantissa : **The decimal part is known as mantissa and is always positive.

E.g, In , the integral part of x is called the characteristic and the decimal part of x is called the mantissa.

For example: In log 3274 = 3.5150, the integral part is 3 i.e., characteristic is 3 and the decimal part is .5150 i.e., mantissa is .5150

**To find the characteristic of common logarithm **:

(a) when the number is greater than 1 i.e., x > 1

In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.

(b) when the number is less than 1 i.e., 0<x<1

In this case the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and is negative.

Instead of -1, -2, etc. we write, etc.

A) 2.875 | B) 3.875 |

C) 4.875 | D) 5.875 |

A) 0.754 | B) 0.854 |

C) 0.954 | D) 0.654 |

Explanation:

log 27 = 1.431

3 log 3 = 1.431

log 3 = 0.477

log 9 = = 2 log 3 = (2 x 0.477) = 0.954

A) 17 | B) 19 |

C) 23 | D) 25 |

Explanation:

=16.85768.

Its characteristics is 16.

Hence, the number of digits in is 17.

A) 5 | B) -5 |

C) 6 | D) -6 |

Explanation:

log (0.0000134). Since there are four zeros between the decimal point and

the first significant digit, the characteristic is –5.