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

##### 1 Answer

Jan 19, 2016

There are no solutions.

#### Explanation:

Use the logarithm rules to simplify either side:

- Left hand side:
#loga+logb=log(ab)# - Right hand side:
#bloga=log(a^b)#

This gives

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

This can be simplified using the following rule:

- If
#loga=logb# , then#a=b#

Giving us:

#(x-1)(x+1)=(x+2)^2#

Distribute both of these.

#x^2-1=x^2+4x+4#

Solve. The

#4x=-5#

#x=-5/4#

**However, this solution is invalid.** Imagine if