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

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

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

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Cancel

\frac{x ^{2} y ^{3}}{x y} : x y^{2}

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

lo g_{3} (m) + lo g_{3} (5) - n

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

4 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 3)

lo g_{10} (x) + 6 lo g_{10} (x + 7)

lo g_{10} (0.401) - lo g_{10} (0.8)

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