Please show as much work as possible Thanks 9 Solve the loga

Please show as much work as possible, Thanks!

(9) Solve the logarithmic equation log11 (z + 1) = log11 (z-1)-log11 (z + 5)

log11(x+1) = log11(x-1) -log11(x+5)

Use the log property: logA - logB = log(A/B)

log11(x+1) = log11(x-1)/(x+5)

Equate the arguments on both sides:

x+1 = (x-1)/(x+5)

(x+1)(x+5) = (x-1)

x^2 +6x +5 = x-1

x^2 +5x +6 =0

Factorise: x^2 +3x +2x +6 =0

x(x+3) +2(x+3) =0

(x+2)(x+3) =0

x=-2 ; x=-3

Solution : x = -3 ,-2-