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Popular >

simplify log_{10}(2500)

Solution

simplify

lo g_{10} (2500)

Solution

2 + 2 lo g_{10} (5)

+1

Decimal Notation

3.39794 \dots

Solution steps

lo g_{10} (2500)

Factor the number:

2500 = 1 0^{2} \cdot 25

= lo g_{10} (1 0^{2} \cdot 25)

Apply log rule:

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

lo g_{10} (1 0^{2} \cdot 25) = lo g_{10} (1 0^{2}) + lo g_{10} (25)

= lo g_{10} (1 0^{2}) + lo g_{10} (25)

Apply log rule:

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

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

= 2 + lo g_{10} (25)

lo g_{10} (25) = 2 lo g_{10} (5)

= 2 + 2 lo g_{10} (5)

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Frequently Asked Questions (FAQ)

What is log_{10}(2500) ?
The solution to log_{10}(2500) is 2+2log_{10}(5)