What is log_{10}((sqrt(5x))/(y^3)) ?

The solution to log_{10}((sqrt(5x))/(y^3)) is log_{10}(sqrt(5x))-3log_{10}(y)

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simplify log_{10}((sqrt(5x))/(y^3))

simplify

lo g_{10} (\frac{5 x}{y ^{3}})

lo g_{10} (5 x) - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{5 x}{y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{5 x}{y ^{3}}) = lo g_{10} (5 x) - lo g_{10} (y^{3})

= lo g_{10} (5 x) - lo g_{10} (y^{3})

Simplify

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

= lo g_{10} (5 x) - 3 lo g_{10} (y)

lo g_{3} (A) + lo g_{3} (B)

15872 ln^{2} (\frac{7}{5})

7 ln (5 c) + \frac{ln ( 5 a )}{4} + \frac{ln ( 5 b )}{4}

\frac{1}{2} lo g_{5} (7) - 2 lo g_{5} (x)

lo g_{10} (5) + lo g_{10} (6) - lo g_{10} (2)

What is log_{10}((sqrt(5x))/(y^3)) ?
The solution to log_{10}((sqrt(5x))/(y^3)) is log_{10}(sqrt(5x))-3log_{10}(y)