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

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

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expand ln((2/(a^3))^4)

expand

ln ((\frac{2}{a ^{3}})^{4})

4 (ln (2) - 3 ln (a))

Solution steps

ln ((\frac{2}{a ^{3}})^{4})

Apply log rule:

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

ln ((\frac{2}{a ^{3}})^{4}) = 4 ln (\frac{2}{a ^{3}})

= 4 ln (\frac{2}{a ^{3}})

Apply log rule:

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

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

= 4 (ln (2) - ln (a^{3}))

Apply log rule:

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

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

= 4 (ln (2) - 3 ln (a))

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

ln (θ (θ + 1) x^{θ - 1} (1 - x))

300 ln (\frac{1}{2})

lo g_{10} (\frac{x}{3 y ^{3}})

ln (\frac{1}{2}) + \frac{π}{6}

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