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Popular >

simplify log_{3}(216)

Solution

simplify

lo g_{3} (216)

Solution

3 + 3 lo g_{3} (2)

+1

Decimal Notation

4.89278 \dots

Solution steps

lo g_{3} (216)

Factor the number:

216 = 3^{3} \cdot 8

= lo g_{3} (3^{3} \cdot 8)

Apply log rule:

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

lo g_{3} (3^{3} \cdot 8) = lo g_{3} (3^{3}) + lo g_{3} (8)

= lo g_{3} (3^{3}) + lo g_{3} (8)

Apply log rule:

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

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

= 3 + lo g_{3} (8)

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

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

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Frequently Asked Questions (FAQ)

What is log_{3}(216) ?
The solution to log_{3}(216) is 3+3log_{3}(2)