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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

\frac{7}{2} lo g_{10} (a) + 8 lo g_{10} (b)

ln (\frac{27 - 10}{9.9 - 10})

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

\frac{7 2}{8} - \frac{5 2}{4} ln (22)

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

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