What is log_{10}(m)+log_{10}(n)-log_{10}(p) ?

The solution to log_{10}(m)+log_{10}(n)-log_{10}(p) is log_{10}((mn)/p)

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simplify log_{10}(m)+log_{10}(n)-log_{10}(p)

simplify

lo g_{10} (m) + lo g_{10} (n) - lo g_{10} (p)

lo g_{10} (\frac{mn}{p})

Solution steps

lo g_{10} (m) + lo g_{10} (n) - lo g_{10} (p)

Apply log rule:

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

lo g_{10} (m) + lo g_{10} (n) = lo g_{10} (mn)

= lo g_{10} (mn) - lo g_{10} (p)

Apply log rule:

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

lo g_{10} (mn) - lo g_{10} (p) = lo g_{10} (\frac{mn}{p})

= lo g_{10} (\frac{mn}{p})

lo g_{4} (\frac{64}{y})

lo g_{b} (80) - lo g_{b} (5)

ln (\frac{e ^{5}}{14})

lo g_{b} (\frac{x ^{2} y}{z ^{4}})

lo g_{b} (\frac{9}{8})

What is log_{10}(m)+log_{10}(n)-log_{10}(p) ?
The solution to log_{10}(m)+log_{10}(n)-log_{10}(p) is log_{10}((mn)/p)