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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

lo g_{7} (3 k)

lo g_{10} (2) + lo g_{10} (4) + lo g_{10} (8)

lo g_{10} (a^{2} b)

ln (1 0^{- 5} \cdot 0.082 \cdot 298)

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