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Sladkaya [172]
2 years ago
11

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

Mathematics
1 answer:
melomori [17]2 years ago
4 0

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.

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.

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