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Popular >

simplify log_{3}(54)

Solution

simplify

lo g_{3} (54)

Solution

3 + lo g_{3} (2)

+1

Decimal Notation

3.63092 \dots

Solution steps

lo g_{3} (54)

Factor the number:

54 = 3^{3} \cdot 2

= lo g_{3} (3^{3} \cdot 2)

Apply log rule:

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

lo g_{3} (3^{3} \cdot 2) = lo g_{3} (3^{3}) + lo g_{3} (2)

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

Apply log rule:

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

lo g_{3} (3^{3}) = 3

= 3 + lo g_{3} (2)

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Frequently Asked Questions (FAQ)

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