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

the answer is x=16/3

Explanation:

:))

Answer 2

9514 1404 393

Answer:

x = 16/3

Explanation:

a) The rewritten equation is ...

`(x-2)/(x+8)=(x-1)/(x+12)`

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b) The solution can be found as ...

`(x-2)/(x+8)-(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=(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)