PLEASE HELP ME!! Tristen solved the equation log 3(x+1) - log 3(x-6) = log 3(2x + 2). Justify each step of solving the equation in Tristen's work below. Are both numbers solutions to the equation? Explain.
Justify each step of solving the equation in Tristen's work.
log 3(x+1) - log 3(x - 6) = log 3(2x+2)
Write the original equation
log 3(x + 1) = log 3(x-6) + log 3(2x + 2) Subtract the same logarithm from each side.
log 3(x + 1) = log 3(x-6)(2x + 2)
Power Property of Logarithms
(x + 1) = (x - 5)(2x+2)
Property of Equality for Exponential Equations
x + 1 = 2x2 - 10x - 12
Divide.
0 = 2x2 - 11x - 13
Subtract x + 1 from each side.
x=6.5 or x = -1
Apply the Zero Product Property.
Are both numbers solutions to the equation? Explain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Only the one solution x = is correct, and it is extraneous
OB. Both solutions are correct, and the solution(s)= is/are extraneous
(Use a comma to separate answers as needed.)
O C. Both solutions are correct, and neither solution is extraneous
Click to select and enter your answer(s).