Definition Of Logarithm

For any ,q > 0 and q ≠ 1 if, r = q^p then logarithm of 'r' to base 'q' is 'p' and it can be written as p = log_qr. Log is the abbreviation for Logarithm.

More About Logarithm

Common Logarithms: Logarithms that use 10 as the base are called common logarithms.
Natural Logarithms: Logarithms with base 'e' are called common logarithms and it is written as y = ln x.
Logarithmic Function: The inverse of exponential function is known as a logarithmic function.
Logarithmic Equation: An equation containing one or more logarithms is called a logarithmic equation.

Video Examples: Logarithm Introduction

 

Example of Logarithm

2⁵ = 32 ⇒ Log₂32 = 5 
1.1² = 1.21 ⇒ Log_1.1121=2

Solved Example on Logarithm

Ques: Which one of the following expresses 2.7⁴ = 53.1 in logarithmic form?

Choices:

A. log_2.74 = 53.1 
B. log₄2.7 = 53.1 
C. log_2.753.1 = 4 
D. log_53.1 2.7 = 4 
Correct Answer: C

Solution:

Step 1: For any q > 0 and q ≠ 1 if r = q^p then logarithm of 'r' to base 'q' is 'p' and it can be written as p = log_qr. 
Step2: From the definition, 2.7⁴ = 53.1 can be expressed in the logarithmic form as log_2.753.1 = 4 .

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