What is ln(((x+2)^2)/(xy^{1/3)}) ?

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

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simplify ln(((x+2)^2)/(xy^{1/3)})

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

\frac{1.16 \cdot 1 0 ^{22}}{0.018}

(x - 1) (x + 4)^{2} - (x - 1)^{2} (x + 4)

3 \cdot (2 x - 6) - [(x - (3 x - 8) + 2) - 1] = 2 - (3 - 2 x)

(4.56 + d) - (4.56 - d) = 0.26425195

- x^{2} + x - 1 = 0

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