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

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

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simplify log_{10}((sqrt(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_{3} (\frac{5}{q ^{2} p})

lo g_{5} (\frac{a ^{8}}{b ^{7} c})

ln (2 e^{- 2 x})

ln (x) - 2 [ln (x + 2) + ln (x - 2)]

ln (\frac{x ^{2} - 1}{x ^{3}})

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