What is log_{10}(x)+2log_{10}(y)-3log_{10}(z) ?

The solution to log_{10}(x)+2log_{10}(y)-3log_{10}(z) is log_{10}((xy^2)/(z^3))

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simplify log_{10}(x)+2log_{10}(y)-3log_{10}(z)

simplify

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

lo g_{10} (\frac{x y ^{2}}{z ^{3}})

Solution steps

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

= lo g_{10} (x) + lo g_{10} (y^{2}) - 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^{2}) = lo g_{10} (x y^{2})

= lo g_{10} (x y^{2}) - 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^{2}) - 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^{2}) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x y ^{2}}{z ^{3}})

= lo g_{10} (\frac{x y ^{2}}{z ^{3}})

\frac{1}{3} ln (x) + 3 ln (y)

lo g_{6} (x) + lo g_{6} (y) + 6 lo g_{6} (z)

lo g_{2} (x + 1) + lo g_{2} (x - 1)

\frac{1}{3} lo g_{2} (5)

lo g_{3} (x - 4) + lo g_{3} (x + 4)

What is log_{10}(x)+2log_{10}(y)-3log_{10}(z) ?
The solution to log_{10}(x)+2log_{10}(y)-3log_{10}(z) is log_{10}((xy^2)/(z^3))