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

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

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

simplify

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

2 ln (x + 1) - ln (x) - ln (x + 2)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x (x + 2)) = ln (x) + ln (x + 2)

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

- (ln (x) + ln (x + 2)) : - ln (x) - ln (x + 2)

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

- 12 ln (3 + 5) + 12 ln (3 + 2)

lo g_{e} (2 e^{3 x})

- 2 ln (y) - ln (x)

4 ln (x - 4) + 5 ln (x - 5) + c

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

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