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

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

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

simplify

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

lo g_{2} (\frac{x}{yz})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

= lo g_{2} (\frac{x}{yz})

ln (\frac{4}{a ^{2} b}) 3

lo g_{3} (\frac{27}{x + 9})

3 [ln (x - 2) + 2 ln (x + 1) - ln (x + 2) - 5 ln (x - 1)]

ln (x^{4}) - ln (x)

lo g_{10} (100 \cdot x)

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