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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (z (z - 1)^{2})

ln (\frac{6.05 + 8.05}{31.8})

lo g_{9} (5) + lo g_{9} (7)

\frac{1}{3} lo g_{b} (x) + 5 lo g_{b} (y) - 2 lo g_{b} (x)

ln (\frac{9 + 61}{10})

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