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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

x x^{2} y y^{3} : x^{3} y^{4}

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

lo g_{10} (\frac{z ^{3}}{x ^{5} y})

ln (x sin (x))

20 lo g_{6} (u) + 5 lo g_{6} (v)

ln (8) + ln (x) + ln (y)

lo g_{9} (\frac{u ^{2}}{s ^{3} t ^{4}})

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