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Popular >

simplify log_{256}(64)

Solution

simplify

lo g_{256} (64)

Solution

\frac{3}{4}

+1

Decimal Notation

0.75

Solution steps

lo g_{256} (64)

Factor the number:

256 = 2^{8}

= lo g_{2^{8}} (64)

Apply log rule:

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

lo g_{2^{8}} (64) = \frac{1}{8} lo g_{2} (64)

= \frac{1}{8} lo g_{2} (64)

Factor the number:

64 = 2^{6}

= \frac{1}{8} lo g_{2} (2^{6})

Apply log rule:

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

lo g_{2} (2^{6}) = 6

= \frac{1}{8} \cdot 6

\frac{1}{8} \cdot 6 = \frac{3}{4}

= \frac{3}{4}

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Frequently Asked Questions (FAQ)

What is log_{256}(64) ?
The solution to log_{256}(64) is 3/4