Key Concepts & Glossary
Key Equations
Definition of the logarithmic function | For , if and only if . |
Definition of the common logarithm | For , if and only if . |
Definition of the natural logarithm | For , if and only if . |
Key Concepts
- The inverse of an exponential function is a logarithmic function, and the inverse of a logarithmic function is an exponential function.
- Logarithmic equations can be written in an equivalent exponential form, using the definition of a logarithm.
- Exponential equations can be written in their equivalent logarithmic form using the definition of a logarithm.
- Logarithmic functions with base b can be evaluated mentally using previous knowledge of powers of b.
- Common logarithms can be evaluated mentally using previous knowledge of powers of 10.
- When common logarithms cannot be evaluated mentally, a calculator can be used.
- Real-world exponential problems with base 10 can be rewritten as a common logarithm and then evaluated using a calculator.
- Natural logarithms can be evaluated using a calculator.
Glossary
- common logarithm
- the exponent to which 10 must be raised to get x; is written simply as .
- logarithm
- the exponent to which b must be raised to get x; written
- natural logarithm
- the exponent to which the number e must be raised to get x; is written as .