Question

Please help, explain in words the steps needed to solve this problem

Answer 1

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.

`log(x) + log(x - 1) = log(x(x - 1)) = log( {x}^(2) - x ) = log(3x + 12)`

Raise both sides to the power of 10 to eliminate the logs, obtaining:

`{x}^(2) - x = 3x + 12`

`{x}^(2) - 4x - 12 = 0`

`(x - 6)(x + 2) = 0`

x = -2 or x = 6. Since x = -2 is extraneous, it follows that x = 6.