What is Algebra? #
Algebra is a branch of mathematics that uses symbols (like x, y) to represent numbers and relationships.
Basic Algebra Concepts #
Variables: Symbols for unknown values (x, y)
Constants: Fixed values (5, 10)
Expression: Combination of numbers & variables → 2x + 3
Equation: Two expressions equal → 2x + 3 = 7
Solving Linear Equation #
Example: #
Solution:
What are Exponents? #
Exponents represent repeated multiplication.
Example: #
Laws of Exponents #
- Product Rule:
a^m × a^n = a^(m+n) - Division Rule:
a^m / a^n = a^(m-n) - Power Rule:
(a^m)^n = a^(m×n) - Zero Power:
a^0 = 1
. What are Logarithms? #
Logarithms are the inverse of exponents.
They answer:
“To what power should the number be raised?”
Example:
Because:
Common Log Rules #
log(a × b) = log(a) + log(b)log(a / b) = log(a) - log(b)log(a^n) = n log(a)
Simple Python Example
import math # Exponent print(2**3) # 8 # Logarithm (base 2) print(math.log2(8)) # 3
- Algebra: Works with variables and equations
- Exponents: Repeated multiplication
- Logarithms: Reverse of exponents
Simple idea:
Exponent → Multiply
Log → Find power