What is log_{10}(x)-3log_{10}(y)+2/3 log_{10}(z) ?

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

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simplify log_{10}(x)-3log_{10}(y)+2/3 log_{10}(z)

simplify

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

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

Solution steps

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

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

\frac{2}{3} lo g_{10} (z) = lo g_{10} (z^{\frac{2}{3}})

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (z^{\frac{2}{3}}) : \frac{2}{3} lo g_{10} (z)

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

Simplify

\frac{2}{3} lo g_{10} (z) : \frac{2 lo g _{10} ( z )}{3}

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

lo g_{10} (56) - lo g_{10} (5 t)

lo g_{5} (\frac{25}{x})

lo g_{b} (\frac{2}{z ^{5} y})

lo g_{4} (64 x^{5})

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