Expanding and Condensing Logarithm
A logarithmic expression can be expanded and condensed using the following Properties of Log:
- Product Rule of Log: logxab = logxa + logxb
- Quotient Rule of Log: logxa/b = logxa – logxb
- Power Rule of Log: logxab = b.logxa
Expanding Log
Log can be expanded in the following manner.
Example: Expand log(2a3b2)
Solution:
log(2a3b2) = log 2 + log a3 + log b2
= log 2 + 3 log a + 2 log b
Condensing Log
A log can be condensed in the following manner just by following the reverse of the properties of log.
Example: Condense log 2 + 3 log a + 2 log b
Solution:
log 2 + 3 log a + 2 log b
= log 2 + log a3 + log b2
= 2a3b2
Logarithm – Definition, Rules , Properties and Examples
A Logarithm is a mathematical function that represents the exponent to which a fixed number, known as the base, must be raised to produce a given number. In other words, it is the inverse operation of exponentiation.
Logarithms are widely used in science, engineering, and mathematics for dealing with very large or very small numbers, as they allow for easier manipulation and comparison of exponential rates of growth or decay. They are foundational in fields such as acoustics, electronics, and in the analysis of algorithms, where they help in understanding the complexity and performance.
Let’s learn logarithms in detail, including logarithmic functions, Logarithm rules, Logarithm properties, Logarithm graphs, and Logarithm examples.
Table of Content
- What is Logarithm?
- Logarithms Meaning
- Exponential to Log Form
- Log to Exponential Form
- Definition of Logarithm | Log Definition
- Logarithm Types
- Common Logarithm
- Natural Logarithm
- Difference between Log and ln | log vs ln
- Rules of Logarithm | Log Rules
- Product Rule of Log
- Quotient Rule of Log
- Power Rule of Log
- Change of Base Rule
- Base Switch Rule
- Equality of Logarithm
- Number Raised to Log
- Negative Log Rule
- Articles related to Logarithms:
- Log 1
- Logaa
- Log 0
- Logarithmic Function
- Expanding and Condensing Logarithm
- Expanding Log
- Condensing Log
- Logarithmic Formulas
- Log Calculator
- Log Table
- Anti Log Table
- Logarithmic Graph
- Properties of Logarithmic Graph
- Solved Examples on Logarithm
- Practice Questions on Logarithm
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