# How do you solve #Log_2 X + Log_2 (X-3) = Log_2 (X^2-12)#?

##### 2 Answers

Use the

#### Explanation:

Log Multiplication Rule:

Therefore

and the given equation:

is equivalent to

This implies

#### Explanation:

First of all, use the fact that for any base, the sum of two logarithms is the logarithm of the product of the arguments. In formulas:

This means that, in your case, we have that

So, the equation becomes

Now, the logarithm is an injective function. This means that two different numbers can't have the same logarithm. Again, in formulas, this means that

In your case,

Which is an equation that we can solve much easily: