What is 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z) ?

The solution to 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z) is log_{10}((\sqrt[3]{x})/(yz^2))

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simplify 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z)

simplify

\frac{1}{3} lo g_{10} (x) - lo g_{10} (y) - 2 lo g_{10} (z)

Solution steps

\frac{1}{3} lo g_{10} (x) - lo g_{10} (y) - 2 lo g_{10} (z)

\frac{1}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{3}})

- 2 lo g_{10} (z) = - lo g_{10} (z^{2})

= lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y) = lo g_{10} (\frac{x ^{\frac{1}{3}}}{y})

= lo g_{10} (\frac{x ^{\frac{1}{3}}}{y}) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (\frac{x ^{\frac{1}{3}}}{y}) - lo g_{10} (z^{2}) = lo g_{10} \frac{\frac{x ^{\frac{1}{3}}}{y}}{z ^{2}}

= lo g_{10} \frac{\frac{x ^{\frac{1}{3}}}{y}}{z ^{2}}

Simplify

\frac{\frac{x ^{\frac{1}{3}}}{y}}{z ^{2}} : \frac{x ^{\frac{1}{3}}}{y z ^{2}}

= lo g_{10} (\frac{x ^{\frac{1}{3}}}{y z ^{2}})

Apply exponent rule:

lo g_{2} (\frac{1}{4}) - lo g_{2} (2 - x)

\frac{1}{2} + 7 lo g_{2} (x) - \frac{3}{2} lo g_{2} (y)

lo g_{10} (π) + 2 lo g_{10} (r)

ln (\frac{1}{x + 8})

lo g_{2} (\frac{393}{7}) + 6

What is 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z) ?
The solution to 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z) is log_{10}((\sqrt[3]{x})/(yz^2))