What is log_{10}(x/(2y)) ?

The solution to log_{10}(x/(2y)) is log_{10}(x)-log_{10}(2)-log_{10}(y)

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simplify log_{10}(x/(2y))

simplify

lo g_{10} (\frac{x}{2 y})

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

Solution steps

lo g_{10} (\frac{x}{2 y})

Apply log rule:

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

lo g_{10} (\frac{x}{2 y}) = lo g_{10} (x) - lo g_{10} (2 y)

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

Simplify

lo g_{10} (2 y) : lo g_{10} (2) + lo g_{10} (y)

= lo g_{10} (x) - (lo g_{10} (2) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (2) + lo g_{10} (y)) = - lo g_{10} (2) - lo g_{10} (y)

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

lo g_{10} (\frac{- 1 1 ^{7}}{- 1 1 ^{3} 5 ^{8}})

lo g_{10} (\frac{9 x}{5})

lo g_{3} (16) + 2 \cdot lo g_{3} (x) - 2 \cdot lo g_{3} (y)

ln (x (x + 7))

lo g_{6} (z^{4} x)

What is log_{10}(x/(2y)) ?
The solution to log_{10}(x/(2y)) is log_{10}(x)-log_{10}(2)-log_{10}(y)