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Popular >

simplify log_{3}(126)

Solution

simplify

lo g_{3} (126)

Solution

2 + lo g_{3} (14)

+1

Decimal Notation

4.40217 \dots

Solution steps

lo g_{3} (126)

Factor the number:

126 = 3^{2} \cdot 14

= lo g_{3} (3^{2} \cdot 14)

Apply log rule:

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

lo g_{3} (3^{2} \cdot 14) = lo g_{3} (3^{2}) + lo g_{3} (14)

= lo g_{3} (3^{2}) + lo g_{3} (14)

Apply log rule:

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

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

= 2 + lo g_{3} (14)

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Frequently Asked Questions (FAQ)

What is log_{3}(126) ?
The solution to log_{3}(126) is 2+log_{3}(14)