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

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

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

simplify

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

lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (a) - lo g_{10} (b)

Solution steps

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

Apply log rule:

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

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

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

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

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

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

6 [ln (z) + ln (z + 8)] - 3 ln (z - 8)

ln (y x)

2 lo g_{y} (3) + lo g_{y} (2)

2 lo g_{10} (x) - 6 lo g_{10} (y)

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

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