Class 9 Math Exercise 3.2 Complete || 9 Class Mathematics Exercise 3.2 Question No.1 To 6

9 Class Math Exercise 3.2 Complete || 9 Class Mathematics Exercise 3.2 Question No.1 To 6

9 Class Math Exercise 3.2 Question No.1
9 Class Math Exercise 3.2 Question No.2
9 Class Math Exercise 3.2 Question No.3
9 Class Math Exercise 3.2 Question No.4
9 Class Math Exercise 3.2 Question No.5
9 Class Math Exercise 3.2 Question No.6

Title: "Logarithm | Characteristics, Mantissa, a^x=y | 9th Class Math | Ex.3.2 Q1-6 | Punjab, KPK, and Federal Board"

Intro: "Welcome to Math Expert! In this comprehensive video, we'll delve into the concept of Logarithm, including its characteristics, mantissa, and the relationship between a^x and y. We'll also solve examples from Exercise 3.2, Question 1-6, covering all boards of Punjab, KPK, and Federal Board. Get ready to master Logarithm!"

Description:

_Logarithm:_

- Definition: Logarithm is the inverse operation of exponentiation.
- Formula: log_a(b) = x, where a^x = b
- Types: Common Logarithm (log), Natural Logarithm (ln)

_Characteristics of Logarithm:_

- Domain: All positive real numbers
- Range: All real numbers
- Base: a (any positive real number)
- Properties: log_a(b) + log_a(c) = log_a(bc), log_a(b) - log_a(c) = log_a(b/c)

_Mantissa:_

- Definition: The decimal part of a logarithm
- Example: log(100) = 2.0000, mantissa = 0.0000

_Relationship between a^x and y:_

- a^x = y = log_a(y) = x
- Applications: Exponential growth and decay, compound interest

_Examples:_

1. Find the logarithm of 1000 with base 10.
2. Evaluate log_2(16).
3. Solve for x in 2^x = 32.
4. Find the mantissa of log(10000).
5. Prove that log_a(b) + log_a(c) = log_a(bc).
6. Simplify log_3(9) + log_3(27).

_Solutions:_

1. log_10(1000) = 3
2. log_2(16) = 4
3. 2^x = 32 = x = 5
4. Mantissa of log(10000) = 0.0000
5. log_a(b) + log_a(c) = log_a(bc)
6. log_3(9) + log_3(27) = log_3(243)

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