What is log_{10}((xy)/z) ?

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

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simplify log_{10}((xy)/z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (4 x) - lo g_{10} (x)

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

lo g_{4} (\frac{16}{x + 4})

lo g_{10} (45) - lo g_{10} (4.5)

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