Common Core · High school
HSF-BF.B.5
High school — Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
A note on this mapping: HSF-BF.B.5 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The 2 skills that cover it
- LogarithmsRead a logarithm as the exponent that answers "b to what power gives x", convert between exponential and logarithmic form, evaluate exact logs, and expand or condense with the product, quotient and power laws.Read the lesson →
- Exponential & Logarithmic EquationsSolve for an exponent by taking a logarithm and for a logarithm by rewriting in exponential form, check every answer against the domain, and use the method on doubling times, pH, decibels and radioactive dating.Read the lesson →
What a student should be able to do
- Convert an equation between exponential form and logarithmic form.
- Evaluate a logarithm exactly, including common and natural logarithms.
- Expand and condense logarithmic expressions with the product, quotient and power laws.
- Use the change-of-base formula and estimate a logarithm from a calculator.
- Solve an exponential equation by matching bases or by taking a logarithm of both sides.
- Solve a logarithmic equation by rewriting it in exponential form or by condensing first.
- Reject a solution that makes the argument of a logarithm zero or negative.
- Find the time for an exponential model to reach a given amount.