What is log_{10}(x)+4log_{10}(y)-3log_{10}(z) ?

The solution to log_{10}(x)+4log_{10}(y)-3log_{10}(z) is log_{10}((xy^4)/(z^3))

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simplify log_{10}(x)+4log_{10}(y)-3log_{10}(z)

simplify

lo g_{10} (x) + 4 lo g_{10} (y) - 3 lo g_{10} (z)

lo g_{10} (\frac{x y ^{4}}{z ^{3}})

Solution steps

lo g_{10} (x) + 4 lo g_{10} (y) - 3 lo g_{10} (z)

Apply log rule:

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

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

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

= lo g_{10} (x y^{4}) - 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^{4}) - 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^{4}) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x y ^{4}}{z ^{3}})

= lo g_{10} (\frac{x y ^{4}}{z ^{3}})

lo g_{3} (\frac{81 x}{x ^{2} + 9})

lo g_{a} (\frac{x ^{2}}{y z ^{3}})

\frac{1}{2} (lo g_{4} (s) + lo g_{4} (t))

2 lo g_{10} (9) + 2 lo g_{10} (x)

ln (x^{6})

What is log_{10}(x)+4log_{10}(y)-3log_{10}(z) ?
The solution to log_{10}(x)+4log_{10}(y)-3log_{10}(z) is log_{10}((xy^4)/(z^3))