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

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

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

simplify

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

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

Solution steps

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

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

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

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

ln (\frac{x ^{p} e ^{(- y)}}{z})

lo g_{10} (\frac{a ^{3} b ^{3}}{c ^{4}})

ln (\frac{5 y ^{2} x}{z ^{3}})

lo g_{7} (\frac{1}{7} a^{3} b)

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