# How do you solve # log(x+2)+log(x-2)=1#?

##### 1 Answer

Feb 25, 2016

#### Explanation:

Simplify the left hand side through the logarithm rule:

#log(a)+log(b)=log(ab)#

Thus, we obtain

#log[(x+2)(x-2)]=1#

Distributed, this gives

#log(x^2-4)=1#

Now, recall that

#log_10(x^2-4)=1#

To undo the logarithm, exponentiate both sides with base

#10^(log_10(x^2-4))=10^1#

#x^2-4=10#

Solve:

#x^2=14#

#x=+-sqrt14#

**Be very careful when solving logarithm functions--always plug your answer back into the original expression.**

Note that the solution

Thus, the only valid solution is