What is log_{10}(2/(ab)) ?

The solution to log_{10}(2/(ab)) is log_{10}(2)-log_{10}(a)-log_{10}(b)

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simplify log_{10}(2/(ab))

simplify

lo g_{10} (\frac{2}{ab})

lo g_{10} (2) - lo g_{10} (a) - lo g_{10} (b)

Solution steps

lo g_{10} (\frac{2}{ab})

Apply log rule:

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

lo g_{10} (\frac{2}{ab}) = lo g_{10} (2) - lo g_{10} (ab)

= lo g_{10} (2) - lo g_{10} (ab)

Simplify

lo g_{10} (ab) : lo g_{10} (a) + lo g_{10} (b)

= lo g_{10} (2) - (lo g_{10} (a) + lo g_{10} (b))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (a) + lo g_{10} (b)) = - lo g_{10} (a) - lo g_{10} (b)

= lo g_{10} (2) - lo g_{10} (a) - lo g_{10} (b)

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

lo g_{7} (2401 x)

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (7)

lo g_{3} (81 x)

ln (\frac{5}{6})

What is log_{10}(2/(ab)) ?
The solution to log_{10}(2/(ab)) is log_{10}(2)-log_{10}(a)-log_{10}(b)