Solved Logarithms Examples
Example 1: Find loga16 + 1/2 loga225 – 2loga2
Solution:
loga16 + 1/2 ✕ 2loga15 – loga22
⇒ loga16 + loga15 – loga4
⇒ loga(16 ✕ 15) – loga4
⇒ loga(16 ✕ 15/4) = loga60
Example 2: Solve logb3 – logb27
Solution:
log23 – log248
⇒ log2(3/48)
⇒ log2(1/16)
⇒ log2(-16)
⇒ -log224
⇒ -4log22 = -4
Example 3: Find x in logbx + logb(x – 3) = logb10
Solution:
Given logbx + logb(x – 3) = logb10
⇒ logb(x)(x – 3) = logb10
⇒ (x)(x – 3) = 10
⇒ x2 – 3x – 10 = 0
⇒ x2 – 5x + 2x – 10 = 0
⇒ x(x – 5) + 2(x – 5)
⇒ (x – 5)(x + 2) = 0
⇒ x = 5, -2
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