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Popular >

simplify log_{10}(400)

Solution

simplify

lo g_{10} (400)

Solution

2 + 2 lo g_{10} (2)

+1

Decimal Notation

2.60205 \dots

Solution steps

lo g_{10} (400)

Factor the number:

400 = 1 0^{2} \cdot 4

= lo g_{10} (1 0^{2} \cdot 4)

Apply log rule:

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

lo g_{10} (1 0^{2} \cdot 4) = lo g_{10} (1 0^{2}) + lo g_{10} (4)

= lo g_{10} (1 0^{2}) + lo g_{10} (4)

Apply log rule:

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

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

= 2 + lo g_{10} (4)

lo g_{10} (4) = 2 lo g_{10} (2)

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

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Frequently Asked Questions (FAQ)

What is log_{10}(400) ?
The solution to log_{10}(400) is 2+2log_{10}(2)