What is expand ln(((x+2)^4y^{1/3})/((w-1)^3)) ?

The solution to expand ln(((x+2)^4y^{1/3})/((w-1)^3)) is 4ln(x+2)+1/3 ln(y)-3ln(w-1)

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expand ln(((x+2)^4y^{1/3})/((w-1)^3))

expand

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})

4 ln (x + 2) + \frac{1}{3} ln (y) - 3 ln (w - 1)

Solution steps

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})

Apply log rule:

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

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}}) = ln ((x + 2)^{4} y^{\frac{1}{3}}) - ln ((w - 1)^{3})

= ln (y^{\frac{1}{3}} (x + 2)^{4}) - ln ((w - 1)^{3})

Apply log rule:

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

ln ((w - 1)^{3}) = 3 ln (w - 1)

= ln ((x + 2)^{4} y^{\frac{1}{3}}) - 3 ln (w - 1)

Apply log rule:

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

ln ((x + 2)^{4} y^{\frac{1}{3}}) = ln ((x + 2)^{4}) + ln (y^{\frac{1}{3}})

= ln ((x + 2)^{4}) + ln (y^{\frac{1}{3}}) - 3 ln (w - 1)

Apply log rule:

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

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

= 4 ln (x + 2) + ln (y^{\frac{1}{3}}) - 3 ln (w - 1)

Apply log rule:

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

ln (y^{\frac{1}{3}}) = \frac{1}{3} ln (y)

= 4 ln (x + 2) + \frac{1}{3} ln (y) - 3 ln (w - 1)

ln (e x y)

ln (1 + e) - ln (2)

ln ∣ x - 1 ∣ - ln ∣ x + 1 ∣

2 ln (x) + ln (2 x + 3)

2 ln (a^{2}) - 3 ln (b)

What is expand ln(((x+2)^4y^{1/3})/((w-1)^3)) ?
The solution to expand ln(((x+2)^4y^{1/3})/((w-1)^3)) is 4ln(x+2)+1/3 ln(y)-3ln(w-1)