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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{2} (4 x^{3})

lo g_{10} (- 2 x)

lo g_{3} (\frac{a b}{12})

2 ln (y) + 3 ln (5 y)

ln (x + h) - ln (x)

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