MA19.PRE.29
Use the inverse relationship between exponents and logarithms to solve problems involving logarithms and exponents. Extend from logarithms with base 2 and 10 to a base of e.
Use the inverse relationship between exponents and logarithms to solve problems involving logarithms and exponents. Extend from logarithms with base 2 and 10 to a base of e.
Unpacked Content
UP:MA19.PRE.29
Vocabulary
- Inverse relationship
- Logarithm
- Natural logarithm
Knowledge
Students know:
- Definition of Logarithm. If bx = y, then logb y = x.
- Restrictions on domain and range of both functions (b > 0, b not equal to 1, y > 0).
- Techniques for creating graphs of exponential and logarithmic functions.
- Situations that can be modeled by exponential and logarithmic functions.
Skills
Students are able to:
- Re-write the equivalent inverse function from an exponential function or logarithm function in various forms (graphs, tables, or equations).
- Model contextual situations using logarithmic and exponential functions.
- Solve exponential and logarithmic equations by isolating the variable.
Understanding
Students understand that:
- Equivalent forms of a function, specifically logarithmic and exponential, may be useful at different times to solve problems.
- Although the algebraic representations look different, the logarithmic form and exponential form of the same relationship are equivalent.
