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Popular >

simplify log_{2}(100)

Solution

simplify

lo g_{2} (100)

Solution

2 + 2 lo g_{2} (5)

+1

Decimal Notation

6.64385 \dots

Solution steps

lo g_{2} (100)

Factor the number:

100 = 2^{2} \cdot 25

= lo g_{2} (2^{2} \cdot 25)

Apply log rule:

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

lo g_{2} (2^{2} \cdot 25) = lo g_{2} (2^{2}) + lo g_{2} (25)

= lo g_{2} (2^{2}) + lo g_{2} (25)

Apply log rule:

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

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

= 2 + lo g_{2} (25)

lo g_{2} (25) = 2 lo g_{2} (5)

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

Popular Examples

x^{2} + 2 x - 36 = 0

0 = 6 x^{2} + 78 x + 216

5x+3<=-72\lor 3x+1>-14

5 x + 3 \leq - 72 or 3 x + 1 > - 14

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Frequently Asked Questions (FAQ)

What is log_{2}(100) ?
The solution to log_{2}(100) is 2+2log_{2}(5)