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

The solution to log_{10}((10)/(x^2sqrt(y))) is 1-2log_{10}(x)-log_{10}(sqrt(y))

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

simplify

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

1 - 2 lo g_{10} (x) - lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (10) = 1

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

= 1 - (2 lo g_{10} (x) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

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

= 1 - 2 lo g_{10} (x) - lo g_{10} (y)

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 8

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 3

ln (\frac{5000}{200})

2 lo g_{10} (7) + 3 lo g_{10} (x)

\frac{1}{7} [ln (x) - ln (x + 4)]

What is log_{10}((10)/(x^2sqrt(y))) ?
The solution to log_{10}((10)/(x^2sqrt(y))) is 1-2log_{10}(x)-log_{10}(sqrt(y))