What is log_{12}(1/2)-log_{12}(8)+log_{12}(w) ?

The solution to log_{12}(1/2)-log_{12}(8)+log_{12}(w) is log_{12}(w/(16))

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simplify log_{12}(1/2)-log_{12}(8)+log_{12}(w)

simplify

lo g_{12} (\frac{1}{2}) - lo g_{12} (8) + lo g_{12} (w)

lo g_{12} (\frac{w}{16})

Solution steps

lo g_{12} (\frac{1}{2}) - lo g_{12} (8) + lo g_{12} (w)

Apply log rule:

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

lo g_{12} (\frac{1}{2}) - lo g_{12} (8) = lo g_{12} (\frac{\frac{1}{2}}{8})

= lo g_{12} (\frac{\frac{1}{2}}{8}) + lo g_{12} (w)

Apply log rule:

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

lo g_{12} (\frac{\frac{1}{2}}{8}) + lo g_{12} (w) = lo g_{12} (\frac{\frac{1}{2}}{8} w)

= lo g_{12} (\frac{\frac{1}{2}}{8} w)

Simplify

\frac{\frac{1}{2}}{8} w : \frac{w}{16}

= lo g_{12} (\frac{w}{16})

lo g_{2} (3) + lo g_{2} (7)

lo g_{2} (10) + lo g_{2} (5)

lo g_{3} (2 x y)

lo g_{10} (\frac{1000 a ^{2}}{c})

3 lo g_{10} (9) + 1 lo g_{10} (x)

What is log_{12}(1/2)-log_{12}(8)+log_{12}(w) ?
The solution to log_{12}(1/2)-log_{12}(8)+log_{12}(w) is log_{12}(w/(16))