What is expand log_{4}(((2j)/(k^5))^3) ?

The solution to expand log_{4}(((2j)/(k^5))^3) is 3(log_{4}(2j)-5log_{4}(k))

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expand log_{4}(((2j)/(k^5))^3)

expand

lo g_{4} ((\frac{2 j}{k ^{5}})^{3})

3 (lo g_{4} (2 j) - 5 lo g_{4} (k))

Solution steps

lo g_{4} ((\frac{2 j}{k ^{5}})^{3})

Apply log rule:

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

lo g_{4} ((\frac{2 j}{k ^{5}})^{3}) = 3 lo g_{4} (\frac{2 j}{k ^{5}})

= 3 lo g_{4} (\frac{2 j}{k ^{5}})

Apply log rule:

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

lo g_{4} (\frac{2 j}{k ^{5}}) = lo g_{4} (2 j) - lo g_{4} (k^{5})

= 3 (lo g_{4} (2 j) - lo g_{4} (k^{5}))

Apply log rule:

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

lo g_{4} (k^{5}) = 5 lo g_{4} (k)

= 3 (lo g_{4} (2 j) - 5 lo g_{4} (k))

lo g_{2} (\frac{1}{x})

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lo g_{\frac{1}{6}} (4) - lo g_{\frac{1}{6}} (9)

ln (\frac{2}{7})

lo g_{10} (2) + 2 lo g_{10} (5)

What is expand log_{4}(((2j)/(k^5))^3) ?
The solution to expand log_{4}(((2j)/(k^5))^3) is 3(log_{4}(2j)-5log_{4}(k))