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Popular >

simplify log_{2}(100000)

Solution

simplify

lo g_{2} (100000)

Solution

5 + 5 lo g_{2} (5)

+1

Decimal Notation

16.60964 \dots

Solution steps

lo g_{2} (100000)

Factor the number:

100000 = 2^{5} \cdot 3125

= lo g_{2} (2^{5} \cdot 3125)

Apply log rule:

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

lo g_{2} (2^{5} \cdot 3125) = lo g_{2} (2^{5}) + lo g_{2} (3125)

= lo g_{2} (2^{5}) + lo g_{2} (3125)

Apply log rule:

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

lo g_{2} (2^{5}) = 5

= 5 + lo g_{2} (3125)

lo g_{2} (3125) = 5 lo g_{2} (5)

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

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Frequently Asked Questions (FAQ)

What is log_{2}(100000) ?
The solution to log_{2}(100000) is 5+5log_{2}(5)