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Popular >

simplify log_{128}(4)

Solution

simplify

lo g_{128} (4)

Solution

\frac{2}{7}

+1

Decimal

0.28571 \dots

Solution steps

lo g_{128} (4)

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (4)

Apply log rule:

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

lo g_{2^{7}} (4) = \frac{1}{7} lo g_{2} (4)

= \frac{1}{7} lo g_{2} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= \frac{1}{7} \cdot 2

\frac{1}{7} \cdot 2 = \frac{2}{7}

= \frac{2}{7}

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Frequently Asked Questions (FAQ)

What is log_{128}(4) ?
The solution to log_{128}(4) is 2/7