Practice Final

Solve the following equations for x
                     a)  log₅ 3.5 = x               b)  log (x + 5) = log ( x -2) - log ( x + 2) solution:

a)  log₅ 3.5 = x (use change of base formula)

  (log(3.5))/(log(5)) = x

  .778385397 = x

b)  log (x + 5) = log ( x -2) - log ( x + 2)

log (x + 5) = log ((x - 2)/(x + 2))

x + 5 = (x - 2)/(x + 2)

(x + 2)(x + 5) = (x - 2)

x² + 7x + 10 = x - 2

x² + 6x + 12 = 0

You can use the quadratic formula, the discriminant or graphing to find
that the answer is an imaginary number. The answer is x = -3 ± i√3

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