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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{a} (u^{7} v^{3})

lo g_{y} (+ 11 lo g_{10} (z))

2 ln (40) - 2 ln (20)

\frac{ln ( \frac{5}{2} )}{5 ln ( 10 )}

lo g_{10} (\frac{x ^{2} y ^{2}}{z ^{15}})

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