Question

Log_6⁡(x+1)+log_6⁡x=1

Answer 1

x = -3, 2

Explanation:

`log_6⁡(x+1)+log_6⁡x=1 \\ \\ log_6⁡ \{x(x+1) \} = 1 \\ \\ x(x + 1) = {6}^(1) \\ \\ {x}^(2) + x = 6 \\ \\ {x}^(2) + x - 6 = 0 \\ \\ {x}^(2) + 3x - 2x - 6 = 0 \\ \\ x(x + 3) - 2(x + 3) = 0 \\ \\ (x + 3)(x - 2) = 0 \\ \\ x + 3 = 0 \: \: or \: \: x - 2 = 0 \\ \\ x = - 3 \: \: or \: \: x = 2 \\ \\ x = - 3, \: \: 2`