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Popular >

simplify log_{128}(2)

Solution

simplify

lo g_{128} (2)

Solution

\frac{1}{7}

+1

Decimal Notation

0.14285 \dots

Solution steps

lo g_{128} (2)

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (2)

Apply log rule:

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

lo g_{2^{7}} (2) = \frac{1}{7} lo g_{2} (2)

= \frac{1}{7} lo g_{2} (2)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= \frac{1}{7} \cdot 1

Multiply the numbers:

\frac{1}{7} \cdot 1 = \frac{1}{7}

= \frac{1}{7}

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Frequently Asked Questions (FAQ)

What is log_{128}(2) ?
The solution to log_{128}(2) is 1/7