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Popular >

simplify log_{3}(45)

Solution

simplify

lo g_{3} (45)

Solution

2 + lo g_{3} (5)

+1

Decimal Notation

3.46497 \dots

Solution steps

lo g_{3} (45)

Factor the number:

45 = 3^{2} \cdot 5

= lo g_{3} (3^{2} \cdot 5)

Apply log rule:

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

lo g_{3} (3^{2} \cdot 5) = lo g_{3} (3^{2}) + lo g_{3} (5)

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

Apply log rule:

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

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

= 2 + lo g_{3} (5)

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Frequently Asked Questions (FAQ)

What is log_{3}(45) ?
The solution to log_{3}(45) is 2+log_{3}(5)