What is expand log_{6}(((ac)/(b^5))^6) ?

The solution to expand log_{6}(((ac)/(b^5))^6) is 6(log_{6}(ac)-5log_{6}(b))

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expand log_{6}(((ac)/(b^5))^6)

expand

lo g_{6} ((\frac{a c}{b ^{5}})^{6})

6 (lo g_{6} (a c) - 5 lo g_{6} (b))

Solution steps

lo g_{6} ((\frac{a c}{b ^{5}})^{6})

Apply log rule:

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

lo g_{6} ((\frac{a c}{b ^{5}})^{6}) = 6 lo g_{6} (\frac{a c}{b ^{5}})

= 6 lo g_{6} (\frac{a c}{b ^{5}})

Apply log rule:

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

lo g_{6} (\frac{a c}{b ^{5}}) = lo g_{6} (a c) - lo g_{6} (b^{5})

= 6 (- lo g_{6} (b^{5}) + lo g_{6} (a c))

Apply log rule:

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

lo g_{6} (b^{5}) = 5 lo g_{6} (b)

= 6 (lo g_{6} (a c) - 5 lo g_{6} (b))

lo g_{5} (y) - 4 (lo g_{5} (r) + 2 lo g_{5} (t))

lo g_{2} (x) - 7 lo g_{2} (y)

ln (\frac{302.35}{273.15})

- lo g_{10} (3.67 \cdot 1 0^{- 4})

ln (- 4 x^{2} e^{- x^{2}})

What is expand log_{6}(((ac)/(b^5))^6) ?
The solution to expand log_{6}(((ac)/(b^5))^6) is 6(log_{6}(ac)-5log_{6}(b))