What is ln((s^2+1)/((s+2)^2)) ?

The solution to ln((s^2+1)/((s+2)^2)) is ln(s^2+1)-2ln(s+2)

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simplify ln((s^2+1)/((s+2)^2))

simplify

ln (\frac{s ^{2} + 1}{( s + 2 ) ^{2}})

ln (s^{2} + 1) - 2 ln (s + 2)

Solution steps

ln (\frac{s ^{2} + 1}{( s + 2 ) ^{2}})

Apply log rule:

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

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

= ln (s^{2} + 1) - ln ((s + 2)^{2})

Apply log rule:

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

ln ((s + 2)^{2}) = 2 ln (s + 2)

= ln (s^{2} + 1) - 2 ln (s + 2)

lo g_{6} (5) + 2 lo g_{6} (x + 1)

\frac{1}{5} (2 ln (2) - ln (3))

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

ln (\frac{1}{64 + 18 - 16 ln ( 16 )})

ln (\frac{201}{200})

What is ln((s^2+1)/((s+2)^2)) ?
The solution to ln((s^2+1)/((s+2)^2)) is ln(s^2+1)-2ln(s+2)