A Difference of Logs
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 32 of 49.
A difference of logs joins the same way, with the quotient rule: subtracting logs divides the insides. log_2(x + 12) - log_2(x) = 2 becomes log_2((x + 12)/x) = 2.
Undo the log by raising 2 to both sides: (x + 12)/x = 4. A fraction equal to a number clears by cross multiplying, which gives x + 12 = 4x. Then 12 = 3x, so x = 4.
A single candidate still gets checked. With x = 4 the inputs are 16 and 4, both positive, and log_2(16) - log_2(4) is 4 minus 2, which is 2. It holds.
Challenge
Solve log_3(x + 6) - log_3(x - 2) = 2 and check your answer.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponentials, Logs & Sequences
1Exponential Functions
Repeated MultiplyingGrowth or DecayDrawing GrowthDrawing DecayRecap: Exponential Functions7Log Equations
Combine, Then UndoA Difference of LogsSame Log Both SidesA False AnswerRecap: Log Equations