# How do you solve #log(x − 3) + log(x − 2) = log(2x + 24)#?

##### 1 Answer

#### Explanation:

Simplify the left side:

Add

Move everything to the left side of the equation so that we can factor:

To factor this, we have to find two numbers that:

- Add up to
#-7# - Multiply up to
#-18# from (#1 * -18# )#

So we have to find a pair of factors of

We know that the factors of

So the factored form becomes:

So

However, these are not our final solutions! We must check our work when solving log equations by plugging it back into the original equation, since you cannot have a log of

Let's check our first solution,

This is true! That means that

Now let's check

Oh no! We cannot take the log of a negative number, but **NOT** a solution.

Finally, the answer is

Hope this helps!