Simplify by writing as a single logarithm & State restrictions:

Question

log(6𝑥^2+5𝑥−6) + log(2x − 3) − log(4𝑥^2 − 9)

Answer 1

since log(ab) = loga - logb, you have
log (2x+3)(3x-2) + log (2x+3) - log (2x-3)(2x+3)
= log(2x+3) + log(3x-2) + log(2x+3) - log(2x-3) - log(2x+3)
= log (2x+3)(3x-2)/(2x-3)

Restrictions: Using the original problem's statement, each quantity must be positive, since logu is defined only if u is positive.
So, using the first term, you need
6x^2+5x-6 > 0
(2x+3)(3x-2) > 0
x must lie in (-∞,-3/2)U(2/3,∞)
Now find the other two intervals and use their intersection, since all three must be positive.