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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{10} (z t) = lo g_{10} (z) + lo g_{10} (t)

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

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (z) + lo g_{10} (t)) = - lo g_{10} (z) - lo g_{10} (t)

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

lo g_{7} (4 d)

lo g_{10} (x) - \frac{1}{4} lo g_{10} (y) + 5 lo g_{10} (z)

ln (\frac{1}{x + 3})

ln (x^{3} e^{- x^{2}})

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