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Popular >

simplify log_{4}(1000)

Solution

simplify

lo g_{4} (1000)

Solution

1 + lo g_{4} (250)

+1

Decimal Notation

4.98289 \dots

Solution steps

lo g_{4} (1000)

Factor the number:

1000 = 4 \cdot 250

= lo g_{4} (4 \cdot 250)

Apply log rule:

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

lo g_{4} (4 \cdot 250) = lo g_{4} (4) + lo g_{4} (250)

= lo g_{4} (4) + lo g_{4} (250)

Apply log rule:

lo g_{a} (a) = 1

lo g_{4} (4) = 1

= 1 + lo g_{4} (250)

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Frequently Asked Questions (FAQ)

What is log_{4}(1000) ?
The solution to log_{4}(1000) is 1+log_{4}(250)