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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

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

ln (\frac{13}{4})

\frac{1}{3} ln (- 1)

lo g_{3} (x + 2) + lo g_{3} (x + 5)

lo g_{9} (x \cdot y \cdot z^{5})

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