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Popular >

simplify log_{1000}(10)

Solution

simplify

lo g_{1000} (10)

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

lo g_{1000} (10)

Factor the number:

1000 = 1 0^{3}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{10} (10) = 1

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

Multiply the numbers:

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

= \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is log_{1000}(10) ?
The solution to log_{1000}(10) is 1/3