Solve the logarithmic equation log11x 1 log11x 1 log11x

Solve the logarithmic equation log_11(x + 1) = log_11(x - 1) - log_11(x + 5).

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

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

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

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

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

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

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

x^2 +5x +6 =0

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

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

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

x= -2 ; x= -3