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Popular >

simplify log_{5}(20)

Solution

simplify

lo g_{5} (20)

Solution

1 + 2 lo g_{5} (2)

+1

Decimal Notation

1.86135 \dots

Solution steps

lo g_{5} (20)

Factor the number:

20 = 5 \cdot 4

= lo g_{5} (5 \cdot 4)

Apply log rule:

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

lo g_{5} (5 \cdot 4) = lo g_{5} (5) + lo g_{5} (4)

= lo g_{5} (5) + lo g_{5} (4)

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

= 1 + lo g_{5} (4)

lo g_{5} (4) = 2 lo g_{5} (2)

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

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Frequently Asked Questions (FAQ)

What is log_{5}(20) ?
The solution to log_{5}(20) is 1+2log_{5}(2)