What is log_{10}(a/(bc)) ?

The solution to log_{10}(a/(bc)) is log_{10}(a)-log_{10}(b)-log_{10}(c)

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simplify log_{10}(a/(bc))

simplify

lo g_{10} (\frac{a}{b c})

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

Solution steps

lo g_{10} (\frac{a}{b c})

Apply log rule:

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

lo g_{10} (\frac{a}{b c}) = lo g_{10} (a) - lo g_{10} (b c)

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

Simplify

lo g_{10} (b c) : lo g_{10} (b) + lo g_{10} (c)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

ln (6) + ln (4) - ln (3)

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