What is log_{2}((5y)/z) ?

The solution to log_{2}((5y)/z) is log_{2}(5)+log_{2}(y)-log_{2}(z)

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simplify log_{2}((5y)/z)

simplify

lo g_{2} (\frac{5 y}{z})

lo g_{2} (5) + lo g_{2} (y) - lo g_{2} (z)

Solution steps

lo g_{2} (\frac{5 y}{z})

Apply log rule:

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

lo g_{2} (\frac{5 y}{z}) = lo g_{2} (5 y) - lo g_{2} (z)

= lo g_{2} (5 y) - lo g_{2} (z)

Simplify

lo g_{2} (5 y) : lo g_{2} (5) + lo g_{2} (y)

= lo g_{2} (5) + lo g_{2} (y) - lo g_{2} (z)

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

lo g_{10} (1000 x^{5})

- \frac{2}{3} ln (3 y)

lo g_{10} (x^{5} y)

lo g_{10} (x (x^{2} + 7)^{- \frac{1}{2}})

What is log_{2}((5y)/z) ?
The solution to log_{2}((5y)/z) is log_{2}(5)+log_{2}(y)-log_{2}(z)