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

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

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

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (x^{3}) + lo g_{10} (y^{2}) = lo g_{10} (x^{3} y^{2})

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

lo g_{g} (\frac{s t ^{6}}{r ^{7}})

lo g_{10} (8) - lo g_{10} (4)

lo g_{10} (y z^{7})

lo g_{4} (6 x^{4})

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