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Numbers, Algebra, Discrete vs Continuous
Logarithm
A logarithm answers which exponent is needed to produce a value.
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Logarithm
Definition
A logarithm asks what exponent is needed to produce a value.
Example:
2^3 = 8
So:
log base 2 of 8 = 3
Logarithm = exponent needed to reach a value.
Logarithm As Inverse Question
Exponent question:
2^3 = ?
Answer:
8
Logarithm question:
2^? = 8
Answer:
3
Exponents produce values; logarithms recover exponents.
Base Matters
The base tells what number is being repeatedly multiplied.
Example:
log base 2 of 8 = 3
because:
2^3 = 8
But:
log base 10 of 100 = 2
because:
10^2 = 100
The logarithm depends on the base.
Simple Examples
Examples:
log base 2 of 16 = 4
log base 3 of 9 = 2
log base 10 of 1000 = 3
Each asks:
base raised to what exponent gives this value?
A logarithm turns a value back into an exponent.
Why Logarithms Matter
Logarithms help describe scale.
Example:
2^10 = 1024
The value 1024 looks large.
But in base 2, it is only exponent 10.
Logarithms measure how many repeated multiplications are needed.
Final Summary
- A logarithm asks which exponent is needed.
- It is connected to exponentiation.
log base 2 of 8 = 3because2^3 = 8.- The base matters.
- Logarithms help describe scale and repeated multiplication.
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Continue the series.
Linear Relationship