What is ln(x^2-1)-5ln(x+1) ?

The solution to ln(x^2-1)-5ln(x+1) is ln((x-1)/((x+1)^4))

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simplify ln(x^2-1)-5ln(x+1)

simplify

ln (x^{2} - 1) - 5 ln (x + 1)

ln (\frac{x - 1}{( x + 1 ) ^{4}})

Solution steps

ln (x^{2} - 1) - 5 ln (x + 1)

Apply log rule:

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

5 ln (x + 1) = ln ((x + 1)^{5})

= ln (x^{2} - 1) - ln ((x + 1)^{5})

Apply log rule:

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

ln (x^{2} - 1) - ln ((x + 1)^{5}) = ln (\frac{x ^{2} - 1}{( x + 1 ) ^{5}})

= ln (\frac{x ^{2} - 1}{( x + 1 ) ^{5}})

Simplify

\frac{x ^{2} - 1}{( x + 1 ) ^{5}} : \frac{x - 1}{( x + 1 ) ^{4}}

= ln (\frac{x - 1}{( x + 1 ) ^{4}})

lo g_{2} (\frac{9}{x + 7})

ln (\frac{x ^{8} cos ^{4} ( x )}{x - 4})

- a (ln ∣ a - l ∣ - ln ∣ a ∣) - l

\frac{1}{2} ln (\frac{386000}{530000})

ln (\frac{50000}{20000})

What is ln(x^2-1)-5ln(x+1) ?
The solution to ln(x^2-1)-5ln(x+1) is ln((x-1)/((x+1)^4))