What is log_{2}((3y)/z) ?

The solution to log_{2}((3y)/z) is log_{2}(3)+log_{2}(y)-log_{2}(z)

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simplify log_{2}((3y)/z)

simplify

lo g_{2} (\frac{3 y}{z})

lo g_{2} (3) + lo g_{2} (y) - lo g_{2} (z)

Solution steps

lo g_{2} (\frac{3 y}{z})

Apply log rule:

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

lo g_{2} (\frac{3 y}{z}) = lo g_{2} (3 y) - lo g_{2} (z)

= lo g_{2} (3 y) - lo g_{2} (z)

Simplify

lo g_{2} (3 y) : lo g_{2} (3) + lo g_{2} (y)

= lo g_{2} (3) + lo g_{2} (y) - lo g_{2} (z)

lo g_{10} (\frac{z ^{3} x ^{4}}{y})

ln (9 x^{3})

lo g_{10} (2 x) lo g_{10} (5) - 1 - 2 lo g_{10} (\frac{5}{2})

ln (x^{3} + 1) - 2 ln (x - 1)

lo g_{5} (\frac{x ^{2}}{x ^{3}})

What is log_{2}((3y)/z) ?
The solution to log_{2}((3y)/z) is log_{2}(3)+log_{2}(y)-log_{2}(z)