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Popular >

simplify log_{10}(500)

Solution

simplify

lo g_{10} (500)

Solution

2 + lo g_{10} (5)

+1

Decimal Notation

2.69897 \dots

Solution steps

lo g_{10} (500)

Factor the number:

500 = 1 0^{2} \cdot 5

= lo g_{10} (1 0^{2} \cdot 5)

Apply log rule:

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

lo g_{10} (1 0^{2} \cdot 5) = lo g_{10} (1 0^{2}) + lo g_{10} (5)

= lo g_{10} (1 0^{2}) + lo g_{10} (5)

Apply log rule:

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

lo g_{10} (1 0^{2}) = 2

= 2 + lo g_{10} (5)

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Frequently Asked Questions (FAQ)

What is log_{10}(500) ?
The solution to log_{10}(500) is 2+log_{10}(5)