What is log_{10}(x)+5log_{10}(y)-3log_{10}(z) ?

The solution to log_{10}(x)+5log_{10}(y)-3log_{10}(z) is log_{10}((xy^5)/(z^3))

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simplify log_{10}(x)+5log_{10}(y)-3log_{10}(z)

simplify

lo g_{10} (x) + 5 lo g_{10} (y) - 3 lo g_{10} (z)

lo g_{10} (\frac{x y ^{5}}{z ^{3}})

Solution steps

lo g_{10} (x) + 5 lo g_{10} (y) - 3 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (x) + lo g_{10} (y^{5}) - 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x y^{5}) - 3 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{10} (z) = lo g_{10} (z^{3})

= lo g_{10} (x y^{5}) - lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (x y^{5}) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x y ^{5}}{z ^{3}})

= lo g_{10} (\frac{x y ^{5}}{z ^{3}})

ln (5 π)

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

lo g_{5} (\frac{1}{x})

lo g_{10} (\frac{y z ^{5}}{x ^{3}})

4 ln (x) + 6 ln (x^{\frac{1}{3}})

What is log_{10}(x)+5log_{10}(y)-3log_{10}(z) ?
The solution to log_{10}(x)+5log_{10}(y)-3log_{10}(z) is log_{10}((xy^5)/(z^3))