What is log_{10}((sqrt(x))/(10y^3)) ?

The solution to log_{10}((sqrt(x))/(10y^3)) is log_{10}(sqrt(x))-1-3log_{10}(y)

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simplify log_{10}((sqrt(x))/(10y^3))

simplify

lo g_{10} (\frac{x}{10 y ^{3}})

lo g_{10} (x) - 1 - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{10 y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x}{10 y ^{3}}) = lo g_{10} (x) - lo g_{10} (10 y^{3})

= lo g_{10} (x) - lo g_{10} (10 y^{3})

Simplify

lo g_{10} (10 y^{3}) : 1 + 3 lo g_{10} (y)

= lo g_{10} (x) - (1 + 3 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (1 + 3 lo g_{10} (y)) = - 1 - 3 lo g_{10} (y)

= lo g_{10} (x) - 1 - 3 lo g_{10} (y)

ln (c d)

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

lo g_{b} (2) + 2 lo g_{b} (5)

ln (e i)

ln (\frac{x}{x ^{2} + 2})

What is log_{10}((sqrt(x))/(10y^3)) ?
The solution to log_{10}((sqrt(x))/(10y^3)) is log_{10}(sqrt(x))-1-3log_{10}(y)