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Popular >

simplify log_{128}(16)

Solution

simplify

lo g_{128} (16)

Solution

\frac{4}{7}

+1

Decimal Notation

0.57142 \dots

Solution steps

lo g_{128} (16)

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (16)

Apply log rule:

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

lo g_{2^{7}} (16) = \frac{1}{7} lo g_{2} (16)

= \frac{1}{7} lo g_{2} (16)

Factor the number:

16 = 2^{4}

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

Apply log rule:

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

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

= \frac{1}{7} \cdot 4

\frac{1}{7} \cdot 4 = \frac{4}{7}

= \frac{4}{7}

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Frequently Asked Questions (FAQ)

What is log_{128}(16) ?
The solution to log_{128}(16) is 4/7