Question

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer
In (x - 2) - In (X + 8) = In (x - 1) - In (x + 12)
Rewrite the given equation without logarithms. Do not solve for x
Solve the equation to find the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution set is { }
(Type an integer or a simplified fraction Use a comma to separate answers as needed)
OB. There are infinitely many solutions
O C. There is no solution

Answer 1

9514 1404 393

Answer:

  x = 16/3

Step-by-step explanation:

a) The rewritten equation is ...

  $\dfrac{x-2}{x+8}=\dfrac{x-1}{x+12}$

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b) The solution can be found as ...

  $\dfrac{x-2}{x+8}-\dfrac{x-1}{x+12}=0\\\\(x-2)(x+12)-(x+8)(x-1)=0 \qquad\text{numerator of the difference}\\\\(x^2+10x-24)-(x^2+7x-8)=0\\\\3x-16=0\qquad\text{simplified}\\\\x=\dfrac{16}{3}\qquad\text{one solution}$

The solution set is {16/3}.

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The applicable rule of logarithms is ...

  log(a) -log(b) = log(a/b)

Answer 2

Answer:

the answer is x=16/3

Step-by-step explanation:

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