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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (x^{5} z)

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

ln (x) - ln (x - 2)

ln (\frac{x}{x - 5})

ln (6) + 3 ln (2)

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