Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.