Question

Solve the following logarithmic equation. log ₄x + log₄(x-6)=2 Select the correct choice below and, if necessary, fill in the answer A. The solution set is. (Type an exact answer.) B. The solution set is the set of real numbers. C. The solution set is the empty set.

Answer 1

`log_(4)(x) + log_(4)(x - 6) = 2`

`log_(4)( {x}^(2) - 6x) = 2`

`{x}^(2) - 6x = 16`

`{x}^(2) - 6x - 16 = 0`

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

x = -2, 8

-2 is an extraneous solution, so x = 8.

a) The solution set is {8}.