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Advanced Mathematics 2200
Relations and Functions
10. NL.SO.2200RF7
10.4 What is a logarithm?
What Is a Logarithm?
A plain-language logarithm definition: what a log is, how it undoes an exponent, and what ln means in math.
What You'll Learn
A logarithm answers the question, what exponent do I raise the base to, to get this number.
The equation log base b of x equals y is just another way of writing b raised to the y equals x.
A common logarithm uses base 10, while a natural logarithm, written ln, uses base e.
Logarithms let us work backward from an exponential result to find the missing exponent.
Logarithms show up in real measurements such as pH, sound decibels, and earthquake magnitude scales.
What You'll Practice
1
Converting exponential equations into logarithmic form
2
Solving for unknown exponents using logarithmic operations
3
Using a calculator to evaluate logarithms with different bases
4
Working through real-world exponential growth problems
Why This Matters
Logarithms unlock your ability to solve exponential equations where the exponent is unknownsomething impossible with basic algebra alone. You'll use logs throughout higher math, science, and finance to model everything from compound interest to population growth to earthquake intensity.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Logarithms
Exponential Equations
Inverse Operations
Exponents
Calculator Skills
Real-World Applications
NL Curriculum Aligned