How do you use the properties of logarithms to expand ln((x^2-1)/x^3)?
1 Answer
Nov 19, 2017
Explanation:
If
ln(a/b) = ln(a) - ln(b)
and:
ln(ab) = ln(a)+ln(b)
Hence we also find:
ln(a^n) = ln(overbrace(a * a * ... * a)^"n times") = overbrace(ln(a) + ln(a) + ... + ln(a))^"n terms" = n ln(a)
So:
ln((x^2-1)/x^3) = ln(x^2-1)-ln(x^3)
color(white)(ln((x^2-1)/x^3)) = ln((x-1)(x+1))-3ln(x)
color(white)(ln((x^2-1)/x^3)) = ln(x-1) + ln(x+1) - 3ln(x)