What is log_{10}(x^2y^3z^4) ?

The solution to log_{10}(x^2y^3z^4) is 2log_{10}(x)+3log_{10}(y)+4log_{10}(z)

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simplify log_{10}(x^2y^3z^4)

simplify

lo g_{10} (x^{2} y^{3} z^{4})

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

Solution steps

lo g_{10} (x^{2} y^{3} z^{4})

Apply log rule:

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

lo g_{10} (x^{2} y^{3} z^{4}) = lo g_{10} (x^{2}) + lo g_{10} (y^{3}) + lo g_{10} (z^{4})

= lo g_{10} (x^{2}) + lo g_{10} (y^{3}) + lo g_{10} (z^{4})

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

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

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

= 2 lo g_{10} (x) + 3 lo g_{10} (y) + 4 lo g_{10} (z)

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

ln (2 x) - ln (x)

lo g_{3} (\frac{x ^{4}}{x - 4})

lo g_{10} (7) + lo g_{10} (3)

ln (x^{12} 6 - x)

What is log_{10}(x^2y^3z^4) ?
The solution to log_{10}(x^2y^3z^4) is 2log_{10}(x)+3log_{10}(y)+4log_{10}(z)