What is log_{10}((sqrt(2x+y))/(y^3)) ?

The solution to log_{10}((sqrt(2x+y))/(y^3)) is log_{10}(sqrt(2x+y))-3log_{10}(y)

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simplify log_{10}((sqrt(2x+y))/(y^3))

simplify

lo g_{10} (\frac{2 x + y}{y ^{3}})

lo g_{10} (2 x + y) - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{2 x + y}{y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{2 x + y}{y ^{3}}) = lo g_{10} (2 x + y) - lo g_{10} (y^{3})

= lo g_{10} (2 x + y) - lo g_{10} (y^{3})

Simplify

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

= lo g_{10} (2 x + y) - 3 lo g_{10} (y)

lo g_{2} (5) + lo g_{2} (2 x - 3)

lo g_{10} (100 y^{4} \cdot \frac{y + 5}{y - 5})

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

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

lo g_{c} (x) + lo g_{c} (y)

What is log_{10}((sqrt(2x+y))/(y^3)) ?
The solution to log_{10}((sqrt(2x+y))/(y^3)) is log_{10}(sqrt(2x+y))-3log_{10}(y)