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Popular >

simplify log_{2}(500)

Solution

simplify

lo g_{2} (500)

Solution

2 + 3 lo g_{2} (5)

+1

Decimal Notation

8.96578 \dots

Solution steps

lo g_{2} (500)

Factor the number:

500 = 2^{2} \cdot 125

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 + lo g_{2} (125)

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

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

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Frequently Asked Questions (FAQ)

What is log_{2}(500) ?
The solution to log_{2}(500) is 2+3log_{2}(5)