Answer:
x=6
Step-by-step explanation:
By the Product Rule of Logarithms, the logarithm of the product of numbers is the sum of the logarithms of the numbers.
[tex] log(x) + log(x - 1) = log(x(x - 1)) = log( {x}^{2} - x ) = log(3x + 12) [/tex]
Raise both sides to the power of 10 to eliminate the logs, obtaining:
[tex] {x}^{2} - x = 3x + 12[/tex]
[tex] {x}^{2} - 4x - 12 = 0[/tex]
[tex](x - 6)(x + 2) = 0[/tex]
x = -2 or x = 6. Since x = -2 is extraneous, it follows that x = 6.
