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

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

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

simplify

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

lo g_{10} (\frac{x}{yz})

Solution steps

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

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)

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

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

Simplify

\frac{\frac{x}{y}}{z} : \frac{x}{yz}

= lo g_{10} (\frac{x}{yz})

\frac{1}{3} ln (x) + ln (y)

\frac{1}{8} ln (y) + ln (z)

ln (x yz)

2 ln (x) - 3 ln (y)

- lo g_{10} (4.1 \times 1 0^{- 3})

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