What is expand ln(((m^5)/(n^2))^3) ?

The solution to expand ln(((m^5)/(n^2))^3) is 3(5ln(m)-2ln(n))

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expand ln(((m^5)/(n^2))^3)

expand

ln ((\frac{m ^{5}}{n ^{2}})^{3})

3 (5 ln (m) - 2 ln (n))

Solution steps

ln ((\frac{m ^{5}}{n ^{2}})^{3})

Apply log rule:

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

ln ((\frac{m ^{5}}{n ^{2}})^{3}) = 3 ln (\frac{m ^{5}}{n ^{2}})

= 3 ln (\frac{m ^{5}}{n ^{2}})

Apply log rule:

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

ln (\frac{m ^{5}}{n ^{2}}) = ln (m^{5}) - ln (n^{2})

= 3 (ln (m^{5}) - ln (n^{2}))

Apply log rule:

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

ln (m^{5}) = 5 ln (m)

= 3 (5 ln (m) - ln (n^{2}))

Apply log rule:

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

ln (n^{2}) = 2 ln (n)

= 3 (5 ln (m) - 2 ln (n))

lo g_{8} (10) - 2 lo g_{8} (3)

lo g_{10} (MN)

lo g_{2} (3 x y^{2})

lo g_{\frac{3}{5}} (\frac{4}{9}) \cdot lo g_{\frac{3}{2}} (\frac{25}{9})

lo g_{10} (\frac{9 b}{10})

What is expand ln(((m^5)/(n^2))^3) ?
The solution to expand ln(((m^5)/(n^2))^3) is 3(5ln(m)-2ln(n))