What is log_{2}(4)+log_{2}(6)-log_{2}(3) ?

The solution to log_{2}(4)+log_{2}(6)-log_{2}(3) is 3

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simplify log_{2}(4)+log_{2}(6)-log_{2}(3)

simplify

lo g_{2} (4) + lo g_{2} (6) - lo g_{2} (3)

3

Solution steps

lo g_{2} (4) + lo g_{2} (6) - lo g_{2} (3)

Apply log rule:

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

lo g_{2} (4) + lo g_{2} (6) = lo g_{2} (4 \cdot 6)

= lo g_{2} (4 \cdot 6) - lo g_{2} (3)

Apply log rule:

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

lo g_{2} (4 \cdot 6) - lo g_{2} (3) = lo g_{2} (\frac{4 \cdot 6}{3})

= lo g_{2} (\frac{4 \cdot 6}{3})

\frac{4 \cdot 6}{3} = 2^{3}

= lo g_{2} (2^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

= 3

\frac{45}{90}

\frac{45}{72}

(4 - 10) (6 - 30)

ln (0.97)

10 x + 4 y - y

What is log_{2}(4)+log_{2}(6)-log_{2}(3) ?
The solution to log_{2}(4)+log_{2}(6)-log_{2}(3) is 3