Drop the logs solve for x

Question

log8 x + log8 (x + 6) = log8 (5x + 12)

Answer 1

By using the product rule of logarithms (loga (m) + loga (n) = loga (m x n)), the equation can be simplified to:

log8 (x(x + 6)) = log8 (5x + 12)

Now, since the bases are the same in both sides of the equation, we can remove the logarithms:

x(x + 6) = 5x + 12

Now, we can expand and simplify the equation:

x^2 + 6x = 5x + 12
x^2 + 6x - 5x - 12 = 0
x^2 + x - 12 = 0

Now we have a quadratic equation, which we can solve by factoring:

(x + 4)(x - 3) = 0

Setting each factor to zero:

x + 4 = 0 OR x - 3 = 0
x = -4 OR x = 3

Therefore, x can be either -4 or 3.