Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Solving exponential and logarithmic equations
Solve exponential and logarithmic equations with domain checks
Problem types
- Exponential equations with a common base
- Solve with a logarithm
- Logarithmic equations
- Solve an exponential equation by rewriting both sides in one base
- Solve a base-10 exponential equation with a coefficient for the variable
Builds on
- Properties of logarithms
- Logarithms as inverses of exponentials
- Rational exponents and radicals · Useful idea
Solving an equation with a fractional exponent raises both sides to the reciprocal power, as same-base exponential equations equate exponents.
- Sums of a finite geometric sequence · Useful idea
Finding how many terms are needed to reach a total from a geometric sum requires solving an exponential equation.
- Rules for a geometric sequence · Useful idea
Finding which term of a geometric sequence reaches a value solves an exponential equation.
Leads to
- Linear growth against exponential growth · See it applied
Finding when an exponential quantity overtakes a linear one means solving an exponential equation with logarithms.
- Quadratic, rational, and exponential constraints · See it applied
When the unknown is a time or count in an exponent, solving the model equation uses logarithms or equal bases.
Related skills
- Solving trigonometric equations · Related idea
Solving for an unknown exponent and solving for an unknown angle both apply an inverse function to isolate the variable.
Open the interactive map to explore lessons and skill connections.