What is log_{10}((sqrt(x))/(100y^5)) ?

The solution to log_{10}((sqrt(x))/(100y^5)) is log_{10}(sqrt(x))-2-5log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^5))

simplify

lo g_{10} (\frac{x}{100 y ^{5}})

lo g_{10} (x) - 2 - 5 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{100 y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x}{100 y ^{5}}) = lo g_{10} (x) - lo g_{10} (100 y^{5})

= lo g_{10} (x) - lo g_{10} (100 y^{5})

Simplify

lo g_{10} (100 y^{5}) : 2 + 5 lo g_{10} (y)

= lo g_{10} (x) - (2 + 5 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 5 lo g_{10} (y)) = - 2 - 5 lo g_{10} (y)

= lo g_{10} (x) - 2 - 5 lo g_{10} (y)

lo g_{10} (\frac{x ^{2} - 1}{x ^{3}})

ln^{2} (4 x)

lo g_{2} (x^{2}) + lo g_{2} (x - 1) - 4

(- \frac{6}{10}) lo g_{2} (\frac{6}{10}) - (\frac{4}{10}) lo g_{2} (\frac{4}{10})

- (\frac{2}{6}) lo g_{2} (\frac{2}{6}) - (\frac{4}{6}) lo g_{2} (\frac{4}{6})

What is log_{10}((sqrt(x))/(100y^5)) ?
The solution to log_{10}((sqrt(x))/(100y^5)) is log_{10}(sqrt(x))-2-5log_{10}(y)