What is expand ln((x^2)/((x+4)^3)) ?

The solution to expand ln((x^2)/((x+4)^3)) is 2ln(x)-3ln(x+4)

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expand ln((x^2)/((x+4)^3))

expand

ln (\frac{x ^{2}}{( x + 4 ) ^{3}})

2 ln (x) - 3 ln (x + 4)

Solution steps

ln (\frac{x ^{2}}{( x + 4 ) ^{3}})

Apply log rule:

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

ln (\frac{x ^{2}}{( x + 4 ) ^{3}}) = ln (x^{2}) - ln ((x + 4)^{3})

= ln (x^{2}) - ln ((x + 4)^{3})

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 + 4)^{3})

Apply log rule:

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

ln ((x + 4)^{3}) = 3 ln (x + 4)

= 2 ln (x) - 3 ln (x + 4)

ln (\frac{x}{y + z})

ln (\frac{x}{x ^{4} y ^{2}})

- ln (3) + ln (2)

ln (\frac{1.011 \cdot 1 0 ^{4}}{1}) \cdot 0.04316

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

What is expand ln((x^2)/((x+4)^3)) ?
The solution to expand ln((x^2)/((x+4)^3)) is 2ln(x)-3ln(x+4)