Logarithms
Understand and apply logarithmic functions and properties
lessons (2)
Introduction to Logarithms
Learn what logarithms are and how they relate to exponents as inverse operations.
Definition of a Logarithm
Understand what logarithms are and how they relate to exponents as inverse operations.
Logarithms are the inverse of exponential functions, answering the question: to what power must the base be raised to get a certain value? Essential for solving exponential equations, logarithms appear in sciences measuring orders of magnitude.
What Students Will Learn
- Convert between exponential and logarithmic forms
- Evaluate logarithms without a calculator
- Apply logarithm properties
- Solve logarithmic equations
- Use logarithms in real-world applications
Frequently Asked Questions
What does a logarithm mean?
$\log_b(x) = y$ means $b^y = x$. For example, $\log_2(8) = 3$ because $2^3 = 8$.
What are the main logarithm properties?
Product: $\log(ab) = \log(a) + \log(b)$. Quotient: $\log(a/b) = \log(a) - \log(b)$. Power: $\log(a^n) = n\log(a)$.
What is the difference between log and ln?
log usually means base 10 (common log). ln means base e (natural log). Both follow the same properties.