[tex] ln({x}^{3} - 4x) - ln(x {}^{2} - 2x ) [/tex]
can be written as;
[tex] ln( \frac{ {x}^{3} - 4x }{ {x}^2 - 2x } ) [/tex]
[tex] ln( \frac{x( {x}^{2 } - 4) }{x(x - 2)} ) = ln( \frac{x(x - 2)(x + 2)}{x(x - 2)} ) [/tex]
Now all you have to do, is divide the numerator and denominator by x and by (x-2)
to get,
[tex] ln( \frac{x(x - 2)(x + 2)}{x(x - 2)} ) = ln( \frac{x + 2}{1} ) = ln(x + 2) [/tex]
We proved that ln(x³-4x)-ln(x²-2) is equal to ln(x+2) :)
