What is log_{2}(2)+log_{2}(9)-log_{2}(6) ?

The solution to log_{2}(2)+log_{2}(9)-log_{2}(6) is log_{2}(3)

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simplify log_{2}(2)+log_{2}(9)-log_{2}(6)

simplify

lo g_{2} (2) + lo g_{2} (9) - lo g_{2} (6)

lo g_{2} (3)

Decimal Notation

1.58496 \dots

Solution steps

lo g_{2} (2) + lo g_{2} (9) - lo g_{2} (6)

Apply log rule:

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

lo g_{2} (2) + lo g_{2} (9) = lo g_{2} (2 \cdot 9)

= lo g_{2} (2 \cdot 9) - lo g_{2} (6)

Apply log rule:

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

lo g_{2} (2 \cdot 9) - lo g_{2} (6) = lo g_{2} (\frac{2 \cdot 9}{6})

= lo g_{2} (\frac{2 \cdot 9}{6})

Cancel

\frac{2 \cdot 9}{6} : 3

= lo g_{2} (3)

lo g_{10} (\frac{100}{a})

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

lo g_{10} (a) + 6 lo g_{10} (r)

ln (\frac{s - 2}{s + 2})

lo g_{10} (a) + 6 lo g_{10} (b)

What is log_{2}(2)+log_{2}(9)-log_{2}(6) ?
The solution to log_{2}(2)+log_{2}(9)-log_{2}(6) is log_{2}(3)