Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(x + 20) - log x = log(x + 2)
A) x = -5, 4
B) x = 4, -5 is extraneous
C) x = 5, 4 is extraneous
D) No solution

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the left side: log(x + 20) - log(x) = log(x + 2) becomes log((x + 20)/x) = log(x + 2). Setting the arguments of the logarithms equal to each other gives (x + 20)/x = x + 2. Solving this equation for x yields x = 4. Testing x = 4 in the original equation confirms it's a valid solution. Testing x = -5 shows it does not satisfy the original equation, making it an extraneous solution.

Solve Using Any Appropriate Method