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Popular >

simplify log_{2}(32000)

Solution

simplify

lo g_{2} (32000)

Solution

8 + 3 lo g_{2} (5)

+1

Decimal Notation

14.96578 \dots

Solution steps

lo g_{2} (32000)

Factor the number:

32000 = 2^{8} \cdot 125

= lo g_{2} (2^{8} \cdot 125)

Apply log rule:

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

lo g_{2} (2^{8} \cdot 125) = lo g_{2} (2^{8}) + lo g_{2} (125)

= lo g_{2} (2^{8}) + lo g_{2} (125)

Apply log rule:

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

lo g_{2} (2^{8}) = 8

= 8 + lo g_{2} (125)

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

= 8 + 3 lo g_{2} (5)

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Frequently Asked Questions (FAQ)

What is log_{2}(32000) ?
The solution to log_{2}(32000) is 8+3log_{2}(5)