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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

\frac{4}{5} ln (x) - 2 ln (y^{4}) + 5 ln (w) - 7 ln (z)

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

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

lo g_{5} (\frac{625}{y})

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