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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

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

lo g_{10} (10 x) + lo g_{10} (20 y) - 1

\frac{1}{3} lo g_{a} (p) + 3 lo g_{a} (q) - 4 lo g_{a} (p)

lo g_{b} (\frac{x y ^{5}}{z ^{4}})

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