Expert: Socrates - 2/12/2006

Question
Need more help understanding steps of logs.
equation is:
log3(m+1) - log3(m-1) = log3 m

I understand quotient property and canceling logs, but show me step by step how to solve this equation. Hopefully lightbulb will go on!

Answer
First , log3(m+1) - log3(m-1) = log3(m+1)/(m-1)

So now the equation becomes log3(m+1)/(m-1) = log3 m

Since (m+1)/(m-1) and m both have the same logarithm , we must have (m+1)/(m-1) = m

Multiply both sides by m-1 and get
m+1 = m^2 - m

simplify to get

m^2-2m-1 = 0

This doesn't factor, so use the quadratic formula to solve for m. This gives 1+2^(1/2) or 1-2^(1/2) as possible values for m. Since you can't take a logarithm of a negative number, the only answer is m = 1+2^(1/2). In words, m is one plus the square root of 2