What is ln((x^2-x-2)/((x+4)^2)) ?

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

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simplify ln((x^2-x-2)/((x+4)^2))

simplify

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

ln (x^{2} - x - 2) - 2 ln (x + 4)

Solution steps

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

Apply log rule:

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

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

= ln (x^{2} - x - 2) - ln ((x + 4)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 4)^{2}) = 2 ln (x + 4)

= ln (x^{2} - x - 2) - 2 ln (x + 4)

\frac{600 ln ( 2 )}{3 ln ( 2 ) - ln ( 3 )}

20 lo g_{10} (\frac{π}{4})

- \frac{1}{3} ln (\frac{1}{2})

lo g_{5} (\frac{d}{125})

ln (\frac{1}{A} e^{x + 6})

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