Question

What are the potential solutions of log₄X + log₄(x+6) = 2? a. x = -2 and x = -8 b. x = -2 and x = 8 c. x = 2 and x = -8 d. x = 2 and x = 8

Answer 1

Explanation:

`log_4(x)+log_4(x+6)=2`

We can remove the plus sign and replace it with multiplication, as stated by the rules of condensing log equations:

`log_4(x^2+6x)=2`

Now we'll use the rule that converts logs to exponents which is to raise the base to the answer and set it equal to the argument:

`4^2=x^2+6x` which is a quadratic that we have to factor. Set the whole thing equal to 0:

`x^2+6x-16=0` which factors to

(x + 8)(x - 2) = 0 so

x = -8 and x = 2, choice c