Question

log6(x-3)+log6(x+2)<2

Answer 1

log6(x-3)+log6(x+2)<2

Answer 2

\[\log_6{(x-3)}+\log_6{(x+2)}<2\quad,\quad x>3\]\[\log_6{(x-3)(x+2)}<2\]\[\log_6{(x-3)(x+2)}<\log_6{36}\]\[(x-3)(x+2)<36\]\[x^2-x-6<36\]\[x^2-x-42<0\]\[(x-7)(x+6)<0\quad\Rightarrow\quad x\in(-6,7)\]\[x\in(-6,7)\quad\wedge\quad x>3\quad\Rightarrow\quad x\in(3,7)\]