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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

\frac{1}{2} lo g_{10} (a) - 3 lo g_{10} (b)

2 lo g_{10} (b) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

3 ln (10) - 4 ln (2) - ln (5)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

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

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