What is log_{2}(10)-log_{2}(5)+log_{2}(11) ?

The solution to log_{2}(10)-log_{2}(5)+log_{2}(11) is log_{2}(22)

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simplify log_{2}(10)-log_{2}(5)+log_{2}(11)

simplify

lo g_{2} (10) - lo g_{2} (5) + lo g_{2} (11)

lo g_{2} (22)

Decimal Notation

4.45943 \dots

Solution steps

lo g_{2} (10) - lo g_{2} (5) + lo g_{2} (11)

Apply log rule:

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

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

= lo g_{2} (\frac{10}{5}) + lo g_{2} (11)

Apply log rule:

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

lo g_{2} (\frac{10}{5}) + lo g_{2} (11) = lo g_{2} (\frac{10}{5} \cdot 11)

= lo g_{2} (\frac{10}{5} \cdot 11)

\frac{10}{5} \cdot 11 = 22

= lo g_{2} (22)

lo g_{10} (y) + lo g_{10} (18)

ln (\frac{13 x ^{8}}{y ^{5}})

lo g_{3} (\frac{1}{2}) + (\frac{1}{2})^{2}

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

What is log_{2}(10)-log_{2}(5)+log_{2}(11) ?
The solution to log_{2}(10)-log_{2}(5)+log_{2}(11) is log_{2}(22)