What is expand log_{4}(((2p)/(q^5))^3) ?

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

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expand log_{4}(((2p)/(q^5))^3)

expand

lo g_{4} ((\frac{2 p}{q ^{5}})^{3})

3 (lo g_{4} (2 p) - 5 lo g_{4} (q))

Solution steps

lo g_{4} ((\frac{2 p}{q ^{5}})^{3})

Apply log rule:

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

lo g_{4} ((\frac{2 p}{q ^{5}})^{3}) = 3 lo g_{4} (\frac{2 p}{q ^{5}})

= 3 lo g_{4} (\frac{2 p}{q ^{5}})

Apply log rule:

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

lo g_{4} (\frac{2 p}{q ^{5}}) = lo g_{4} (2 p) - lo g_{4} (q^{5})

= 3 (lo g_{4} (2 p) - lo g_{4} (q^{5}))

Apply log rule:

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

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

= 3 (lo g_{4} (2 p) - 5 lo g_{4} (q))

lo g_{5} (\frac{25}{x + 6})

ln (y) + ln (x + 1)

lo g_{81} (\frac{( x - 5 )}{3 ( x + 4 ) ^{5}})

lo g_{9} (5) + lo g_{9} (x + 1)

lo g_{b} (mn)

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