What is simplify-ln(x)+ln(((x-3)^2)/(x+1)) ?

The solution to simplify-ln(x)+ln(((x-3)^2)/(x+1)) is ln(((x-3)^2)/(x(x+1)))

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simplify-ln(x)+ln(((x-3)^2)/(x+1))

simplify

- ln (x) + ln (\frac{( x - 3 ) ^{2}}{x + 1})

ln (\frac{( x - 3 ) ^{2}}{x ( x + 1 )})

Solution steps

- ln (x) + ln (\frac{( x - 3 ) ^{2}}{x + 1})

Apply log rule:

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

ln (\frac{( x - 3 ) ^{2}}{x + 1}) - ln (x) = ln (\frac{\frac{( x - 3 ) ^{2}}{x + 1}}{x})

= ln (\frac{\frac{( x - 3 ) ^{2}}{x + 1}}{x})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{( x - 3 ) ^{2}}{x ( x + 1 )})

- \frac{ln ( 42 )}{ln ( 7 ) - ln ( 6 )}

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

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

ln (\frac{x ^{8} x ^{2} + 2}{( x + 2 ) ^{3}})

lo g_{4} (3 2 \cdot 5)

What is simplify-ln(x)+ln(((x-3)^2)/(x+1)) ?
The solution to simplify-ln(x)+ln(((x-3)^2)/(x+1)) is ln(((x-3)^2)/(x(x+1)))