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Popular >

simplify log_{3}(75)

Solution

simplify

lo g_{3} (75)

Solution

1 + 2 lo g_{3} (5)

+1

Decimal Notation

3.92994 \dots

Solution steps

lo g_{3} (75)

Factor the number:

75 = 3 \cdot 25

= lo g_{3} (3 \cdot 25)

Apply log rule:

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

lo g_{3} (3 \cdot 25) = lo g_{3} (3) + lo g_{3} (25)

= lo g_{3} (3) + lo g_{3} (25)

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

= 1 + lo g_{3} (25)

lo g_{3} (25) = 2 lo g_{3} (5)

= 1 + 2 lo g_{3} (5)

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Frequently Asked Questions (FAQ)

What is log_{3}(75) ?
The solution to log_{3}(75) is 1+2log_{3}(5)