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Popular >

simplify log_{100}(1000)

Solution

simplify

lo g_{100} (1000)

Solution

\frac{3}{2}

+1

Decimal Notation

1.5

Solution steps

lo g_{100} (1000)

Factor the number:

100 = 1 0^{2}

= lo g_{1 0^{2}} (1000)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{1 0^{2}} (1000) = \frac{1}{2} lo g_{10} (1000)

= \frac{1}{2} lo g_{10} (1000)

Factor the number:

1000 = 1 0^{3}

= \frac{1}{2} lo g_{10} (1 0^{3})

Apply log rule:

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

lo g_{10} (1 0^{3}) = 3

= \frac{1}{2} \cdot 3

\frac{1}{2} \cdot 3 = \frac{3}{2}

= \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is log_{100}(1000) ?
The solution to log_{100}(1000) is 3/2