9 a Solve the equation and check the answers 6 points Log2 2

9) a) Solve the equation and check the answers.                                                                           (6 points)

Log₂ (2-x) + log ₂ (-x) = 3

b) Solve for x   2^x = 5 ^x-2                                                                                    (6 points)                      

Solution

9.a. log₂(2-x) + log₂(-x)=3

      log₂(x(x-2))=3

x²-2x=8

x²-2x-8=0

(x-4)(x+2)=0

x=4,-2

If we plug x=4,we will get negative values and log cant take negative values. Hence the correct answer is x=-2