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Popular >

simplify log_{2}(5000)

Solution

simplify

lo g_{2} (5000)

Solution

3 + 4 lo g_{2} (5)

+1

Decimal Notation

12.28771 \dots

Solution steps

lo g_{2} (5000)

Factor the number:

5000 = 2^{3} \cdot 625

= lo g_{2} (2^{3} \cdot 625)

Apply log rule:

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

lo g_{2} (2^{3} \cdot 625) = lo g_{2} (2^{3}) + lo g_{2} (625)

= lo g_{2} (2^{3}) + lo g_{2} (625)

Apply log rule:

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

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

= 3 + lo g_{2} (625)

lo g_{2} (625) = 4 lo g_{2} (5)

= 3 + 4 lo g_{2} (5)

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Frequently Asked Questions (FAQ)

What is log_{2}(5000) ?
The solution to log_{2}(5000) is 3+4log_{2}(5)