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

Please Help Explain In Words The Steps Needed To Solve This Problem class=

Sagot :

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.

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