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Popular >

simplify log_{5}(500)

Solution

simplify

lo g_{5} (500)

Solution

3 + 2 lo g_{5} (2)

+1

Decimal Notation

3.86135 \dots

Solution steps

lo g_{5} (500)

Factor the number:

500 = 5^{3} \cdot 4

= lo g_{5} (5^{3} \cdot 4)

Apply log rule:

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

lo g_{5} (5^{3} \cdot 4) = lo g_{5} (5^{3}) + lo g_{5} (4)

= lo g_{5} (5^{3}) + lo g_{5} (4)

Apply log rule:

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

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

= 3 + lo g_{5} (4)

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

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

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simplify (14)/(-3)simplify

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Frequently Asked Questions (FAQ)

What is log_{5}(500) ?
The solution to log_{5}(500) is 3+2log_{5}(2)