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

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

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

simplify

lo g_{10} (x) - lo g_{10} (y) - 2 lo g_{10} (z)

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

Solution steps

lo g_{10} (x) - lo g_{10} (y) - 2 lo g_{10} (z)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

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

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

Simplify

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

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

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