Solving log₂(x) + log₂(x - 3) = 2

Algebra 2 · Axiom Academy

Combine two logarithms with the Product Property, convert to exponential form, then check for extraneous solutions. Solve for x : . Combine the logarithms using the Product Property, convert to exponential form, then check every candidate solution for domain validity. Valid — both arguments are positive. Extraneous — both arguments are negative, so this is undefined. Nice work! You solved a logarithmic equation using log properties and confirmed which candidate solution actually works. Remember: Combine same-base logs with the Product Property: merges two logs into one. Convert to exponential form: means A = b^C — this turns a log equation into an algebraic one. Solve the resulting equation: here that meant factoring the quadratic x^2-3x-4=0 into (x-4)(x+1)=0 . Always check every candidate in the ORIGINAL equation: logarithmic equations can produce extraneous solutions. Domain restrictions matter: a logarithm is only defined for a positive argument, so x=-1 had to be rejected. Here, x=-1 is extraneous because it makes the argument of a logarithm negative — always verify your answers when solving logarithmic equations.

This is the written version of the interactive lesson above. See the full Algebra 2 course.