What is log_{2}(x*y*z^3) ?

The solution to log_{2}(x*y*z^3) is log_{2}(x)+log_{2}(y)+3log_{2}(z)

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simplify log_{2}(xyz^3)

simplify

lo g_{2} (x \cdot y \cdot z^{3})

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

Solution steps

lo g_{2} (x y z^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Simplify

lo g_{2} (z^{3}) : 3 lo g_{2} (z)

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

- \frac{1}{3} lo g_{10} (\frac{1}{3}) - \frac{2}{3} lo g_{10} (\frac{2}{3})

lo g_{2} (225) - lo g_{2} (5) + lo g_{2} (3)

lo g_{3} (x^{2}) + lo g_{3} (25)

3 lo g_{10} (7 x) - 4 lo g_{10} (7 y)

lo g_{2} (\frac{1}{m})

What is log_{2}(x*y*z^3) ?
The solution to log_{2}(x*y*z^3) is log_{2}(x)+log_{2}(y)+3log_{2}(z)