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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

ln \frac{2}{( \frac{3}{2} ) ^{\frac{1}{4}}}

3 lo g_{3} (x) + 9 lo g_{3} (z)

lo g_{\frac{1}{2}} (\frac{8}{15})

5 ln (x) + 4 ln (y) - 3 ln (z)

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