Log(x+1)−log(x−8)=log(10)

How do i solve this?

9514 1404 393

  x = 9

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a) -log(b) = log(a/b)

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Use the rules of logarithms to simplify the left side to a single log, then take the antilogs and solve the resulting equation.

  log(x+1) -log(x-8) = log(10)

  log((x+1)/(x-8)) = log(10)

  (x +1)/(x -8) = 10 . . . . . . . take antilogs

  x +1 = 10(x -8) . . . . multiply by x-8

  81 = 9x . . . . . . . add 81-x, simplify

  9 = x . . . . . . . . . divide by 9

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When the equation is rewritten to the form f(x) = 0, the x-intercept is the solution.

207/8 is the right