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Popular >

simplify log_{2}(2000)

Solution

simplify

lo g_{2} (2000)

Solution

4 + 3 lo g_{2} (5)

+1

Solution steps

lo g_{2} (2000)

Factor the number:

2000 = 2^{4} \cdot 125

= lo g_{2} (2^{4} \cdot 125)

Apply log rule:

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

lo g_{2} (2^{4} \cdot 125) = lo g_{2} (2^{4}) + lo g_{2} (125)

= lo g_{2} (2^{4}) + lo g_{2} (125)

Apply log rule:

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

lo g_{2} (2^{4}) = 4

= 4 + lo g_{2} (125)

lo g_{2} (125) = 3 lo g_{2} (5)

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

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Frequently Asked Questions (FAQ)

What is log_{2}(2000) ?
The solution to log_{2}(2000) is 4+3log_{2}(5)