What is log_{2}(20)+log_{2}(50) ?

The solution to log_{2}(20)+log_{2}(50) is 3log_{2}(10)

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simplify log_{2}(20)+log_{2}(50)

simplify

lo g_{2} (20) + lo g_{2} (50)

3 lo g_{2} (10)

Decimal Notation

9.96578 \dots

Solution steps

lo g_{2} (20) + lo g_{2} (50)

Apply log rule:

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

lo g_{2} (20) + lo g_{2} (50) = lo g_{2} (20 \cdot 50)

= lo g_{2} (20 \cdot 50)

Multiply the numbers:

20 \cdot 50 = 1000

= lo g_{2} (1000)

Factor the number:

1000 = 1 0^{3}

= lo g_{2} (1 0^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{2} (1 0^{3}) = 3 lo g_{2} (10)

= 3 lo g_{2} (10)

lo g_{2} (\frac{4}{y})

lo g_{b} (\frac{x ^{2} y}{z ^{8}})

ln (\frac{1}{2}) + ln (\frac{2}{3}) + ln (\frac{3}{5})

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

What is log_{2}(20)+log_{2}(50) ?
The solution to log_{2}(20)+log_{2}(50) is 3log_{2}(10)