[tex]log_3(x+2)=log_3(2x^2-1)\\3^{log_3(x+2)}=3^{log_3(2x^2-1)}\\x+2=2x^2-1\\-x -2 -x -2\\0=2x^2-x-3\\2*-3=-6\\Test factors -3 and 2:\\-3*2=-6, -3+2=-1\\(x-3)(x+2)=0\\Use slide and divide with 2:\\(x-3/2)(x+2/2)=0\\=>\\(2x-3)(x+1)=0\\Set both equal to 0:\\x+1=0\\x=-1\\2x-3=0\\2x=3\\/2 /2\\x=3/2\\[/tex]
Answer:
x=-1, 3/2
