Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Logarithms as inverses of exponentials
Use logarithms as inverses of exponential functions
Problem types
- Logarithms of reciprocals, roots and decimals
- Read a logarithm
- Logarithms
- Features of exponential and logarithmic graphs
- Choose the graph of a logarithm with a base between 0 and 1
Builds on
- Finding an inverse function
- Building an exponential model
- Shifts, stretches, and reflections of graphs · Useful idea
The graph of a logarithm is shifted, stretched and reflected by the same transformations.
- Rearranging a formula · Useful idea
Solving an exponential formula for the exponent rewrites it as a logarithm.
- Place value of large whole numbers · Earlier idea
A number with n digits is between 10 to the power n - 1 and 10 to the power n, so counting digits estimates its base-10 logarithm.
Leads to
- Solving exponential and logarithmic equations
- Properties of logarithms
- Linear growth against exponential growth · See it applied
The time at which an exponential overtakes another quantity is found by taking a logarithm.
Related skills
- Values a rational expression excludes · Related idea
A rational expression excludes zeros of the denominator and a logarithm excludes nonpositive inputs, both domain restrictions read from the expression.
- Working in scientific notation · Related idea
Scientific notation writes numbers as powers of ten, and a base-ten logarithm is that exponent.
- Inverse trigonometric functions · Shared foundations
- Checking a model against evidence · Shared foundations
- Quadratic, rational, and exponential constraints · Shared foundations
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