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Popular >

simplify log_{2}(120)

Solution

simplify

lo g_{2} (120)

Solution

3 + lo g_{2} (15)

+1

Decimal Notation

6.90689 \dots

Solution steps

lo g_{2} (120)

Factor the number:

120 = 2^{3} \cdot 15

= lo g_{2} (2^{3} \cdot 15)

Apply log rule:

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

lo g_{2} (2^{3} \cdot 15) = lo g_{2} (2^{3}) + lo g_{2} (15)

= lo g_{2} (2^{3}) + lo g_{2} (15)

Apply log rule:

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

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

= 3 + lo g_{2} (15)

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Frequently Asked Questions (FAQ)

What is log_{2}(120) ?
The solution to log_{2}(120) is 3+log_{2}(15)