Solve the following logarithmic equation. Show step by step work.

Question

Solve the following logarithmic equation. Show step by step work.

log4 (𝑥 − 3) = 2 − log4 (𝑥 + 12)

Answer 1

log (ab) = log (a) + log (b). so

log₄(x - 3) + log₄ ( x + 12) = 2

then log₄ (x -3)(x +12) = 2

Now convert to exponential form

4² = (x -3)(x + 12)

16 = x² + 9x -36

0 = x² + 9x -52 = (x + 13)(x - 4)------>. x= -13 or 4. but check if answers work in the orig. problem

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