Question

Show that ln(x^3 "-4x)" − ln(x^2 "-2x)=" ln(x + 2).

Answer 1

`ln({x}^(3) - 4x) - ln(x {}^(2) - 2x )`

can be written as;

`ln( \frac{ {x}^(3) - 4x }{ {x}^2 - 2x } )`

`ln( \frac{x( {x}^(2 ) - 4) }{x(x - 2)} ) = ln( (x(x - 2)(x + 2))/(x(x - 2)) )`

Now all you have to do, is divide the numerator and denominator by x and by (x-2)

to get,

`ln( (x(x - 2)(x + 2))/(x(x - 2)) ) = ln( (x + 2)/(1) ) = ln(x + 2)`

We proved that ln(x³-4x)-ln(x²-2) is equal to ln(x+2) :)