How do you solve Log(x+2) - log(x-2) = log(3)?

1 Answer
Sep 6, 2015

x=4

Explanation:

First we simplify the left side by using the rule: log (a) - log(b) = log(a/b)

log(x+2) - log(x-2) = log(3)

log((x+2)/(x-2)) = log(3)

Then, we apply the rule: log(a) = b <=> 10^b = a

10^log(3) = (x+2)/(x-2)

Then, we can apply the rule: 10^log(k) = k

3 = (x+2)/(x-2)

Now we can just solve the equation:

3x-6 = x+2

2x=8

x=4


Alternatively, we can skip a lot of steps by taking a shortcut:

Since log() is a one-to-one function, log(a) = log(b) means a=b.

log(x+2) - log(x-2) = log(3)

log((x+2)/(x-2)) = log(3)

(x+2)/(x-2) = 3

x+2=3x-6

8=2x

4=x