What is 2ln(a-b)-ln(a^2-b^2) ?

The solution to 2ln(a-b)-ln(a^2-b^2) is ln((a-b)/(a+b))

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simplify 2ln(a-b)-ln(a^2-b^2)

simplify

2 ln (a - b) - ln (a^{2} - b^{2})

ln (\frac{a - b}{a + b})

Solution steps

2 ln (a - b) - ln (a^{2} - b^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (a - b) = ln ((a - b)^{2})

= ln ((a - b)^{2}) - ln (a^{2} - b^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((a - b)^{2}) - ln (a^{2} - b^{2}) = ln (\frac{( a - b ) ^{2}}{a ^{2} - b ^{2}})

= ln (\frac{( a - b ) ^{2}}{a ^{2} - b ^{2}})

Simplify

\frac{( a - b ) ^{2}}{a ^{2} - b ^{2}} : \frac{a - b}{a + b}

= ln (\frac{a - b}{a + b})

\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)

ln (2 a x)

lo g_{10} (3 x y)

ln (\frac{386}{530})

9 ln (a) - 7 ln (b)

What is 2ln(a-b)-ln(a^2-b^2) ?
The solution to 2ln(a-b)-ln(a^2-b^2) is ln((a-b)/(a+b))