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Algebra 2
14. MA.912.AR.5.2
14.1 Solving logarithmic equations
Solving Logarithmic Equations
Solve a logarithmic equation by condensing to one logarithm, rewriting in exponential form, solving, and checking the domain.
What You'll Learn
A logarithmic equation has the variable inside a logarithm, like log base 2 of x equals 3.
Condense multiple logarithms into one using the log rules.
Rewrite log base b of x equals y as b to the power y equals x to remove the logarithm.
Solve the resulting equation for the variable.
Check every solution: the argument of each logarithm must be positive.
What You'll Practice
1
Combining logs with addition and subtraction using quotient and product rules
2
Solving equations with logs on both sides by equating arguments
3
Converting single-log equations to exponential form
4
Factoring quadratic equations from combined logarithmic expressions
5
Rejecting invalid solutions that create negative logarithm arguments
Why This Matters
Solving logarithmic equations is essential for modeling exponential growth and decay in science, finance, and engineering. You'll use these skills in calculus, chemistry (pH calculations), and any field involving exponential relationships.
Before You Start — Make Sure You Can:
This Unit Includes
6 Video lessons
Practice exercises
Learning resources
Skills
Logarithms
Product Rule
Quotient Rule
Power Rule
Exponential Form
Quadratic Equations
Solution Verification
FL Curriculum Aligned