What is ln((e^c)/((x+1)^2)) ?

The solution to ln((e^c)/((x+1)^2)) is c-2ln(x+1)

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simplify ln((e^c)/((x+1)^2))

simplify

ln (\frac{e ^{c}}{( x + 1 ) ^{2}})

c - 2 ln (x + 1)

Solution steps

ln (\frac{e ^{c}}{( x + 1 ) ^{2}})

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{c}) = c ln (e)

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

Apply log rule:

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

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

= c ln (e) - 2 ln (x + 1)

c ln (e) = c

= c - 2 ln (x + 1)

ln (\frac{λ ^{x} e ^{- λ}}{x !})

ln (\frac{ln ( x )}{sin ( x )})

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

210 ln (2) + 210 ln (3 x - 2 y)

- ln (\frac{2}{2}) \cdot \frac{2}{2}