MA19.PRE.29

Mathematics (2019) Grade(s): 09-12 - Precalculus

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.

Unpacked Content

Knowledge

Students know:

Definition of Logarithm. If b^{x^{= 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.

Vocabulary

Inverse relationship
Logarithm
Natural logarithm

Aligned Learning Resources

Logarithms: Undo the Exponential

Solving Exponential and Logarithmic Equations

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