What is expand log_{10}((xy^4)/(z^5)) ?

The solution to expand log_{10}((xy^4)/(z^5)) is log_{10}(x)+4log_{10}(y)-5log_{10}(z)

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expand log_{10}((xy^4)/(z^5))

expand

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x y ^{4}}{z ^{5}}) = lo g_{10} (x y^{4}) - lo g_{10} (z^{5})

= lo g_{10} (x y^{4}) - lo g_{10} (z^{5})

Apply log rule:

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

lo g_{10} (z^{5}) = 5 lo g_{10} (z)

= lo g_{10} (x y^{4}) - 5 lo g_{10} (z)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (x y^{4}) = lo g_{10} (x) + lo g_{10} (y^{4})

= lo g_{10} (x) + lo g_{10} (y^{4}) - 5 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

= lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{10} (\frac{p ^{3} + q}{1000})

lo g_{4} (\frac{x ^{2}}{5})

ln (x^{7}) - ln (x)

lo g_{10} (6) + lo g_{10} (5)

lo g_{7} (x y^{3})

What is expand log_{10}((xy^4)/(z^5)) ?
The solution to expand log_{10}((xy^4)/(z^5)) is log_{10}(x)+4log_{10}(y)-5log_{10}(z)