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Popular >

simplify log_{2}(54)

Solution

simplify

lo g_{2} (54)

Solution

1 + 3 lo g_{2} (3)

+1

Decimal Notation

5.75488 \dots

Solution steps

lo g_{2} (54)

Factor the number:

54 = 2 \cdot 27

= lo g_{2} (2 \cdot 27)

Apply log rule:

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

lo g_{2} (2 \cdot 27) = lo g_{2} (2) + lo g_{2} (27)

= lo g_{2} (2) + lo g_{2} (27)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (27)

lo g_{2} (27) = 3 lo g_{2} (3)

= 1 + 3 lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is log_{2}(54) ?
The solution to log_{2}(54) is 1+3log_{2}(3)