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Popular >

simplify log_{1000}(100)

Solution

simplify

lo g_{1000} (100)

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

lo g_{1000} (100)

Factor the number:

1000 = 1 0^{3}

= lo g_{1 0^{3}} (100)

Apply log rule:

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

lo g_{1 0^{3}} (100) = \frac{1}{3} lo g_{10} (100)

= \frac{1}{3} lo g_{10} (100)

Factor the number:

100 = 1 0^{2}

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

Apply log rule:

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

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

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

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

= \frac{2}{3}

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Frequently Asked Questions (FAQ)

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