Math
Solving log equations.
Definition
Finding the value of the variable in equations that contain logarithms. Techniques include converting to exponential form, using logarithm properties to combine or expand logs, and checking for extraneous solutions (since log arguments must be positive).
How it works · 4 phases
Step by step.
- Use logarithm properties to combine logs on each side into a single logarithm.
- Convert the logarithmic equation to exponential form.
- Solve the resulting equation for the variable.
- Check all solutions to ensure the arguments of every original logarithm are positive.
Examples
Real-world.
- 1 log₂(x) = 5 → x = 2⁵ = 32
- 2 log(x) + log(x−3) = 1 → log(x(x−3)) = 1 → x(x−3) = 10 → x = 5 (x = −2 is extraneous)