What is log_{10}((2u)/(3v)) ?

The solution to log_{10}((2u)/(3v)) is log_{10}(2)+log_{10}(u)-log_{10}(3)-log_{10}(v)

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simplify log_{10}((2u)/(3v))

simplify

lo g_{10} (\frac{2 u}{3 v})

lo g_{10} (2) + lo g_{10} (u) - lo g_{10} (3) - lo g_{10} (v)

Solution steps

lo g_{10} (\frac{2 u}{3 v})

Apply log rule:

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

lo g_{10} (\frac{2 u}{3 v}) = lo g_{10} (2 u) - lo g_{10} (3 v)

= lo g_{10} (2 u) - lo g_{10} (3 v)

lo g_{10} (2 u) = lo g_{10} (2) + lo g_{10} (u)

lo g_{10} (3 v) = lo g_{10} (3) + lo g_{10} (v)

= lo g_{10} (2) + lo g_{10} (u) - (lo g_{10} (3) + lo g_{10} (v))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (3) + lo g_{10} (v)) = - lo g_{10} (3) - lo g_{10} (v)

= lo g_{10} (2) + lo g_{10} (u) - lo g_{10} (3) - lo g_{10} (v)

14 + lo g_{10} (\frac{2 \cdot 0.0105 \cdot 10}{500})

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{9}})

ln (x e^{2 x})

4 lo g_{c} (x) - 6 lo g_{c} (y^{5})

What is log_{10}((2u)/(3v)) ?
The solution to log_{10}((2u)/(3v)) is log_{10}(2)+log_{10}(u)-log_{10}(3)-log_{10}(v)