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Popular >

simplify log_{64}(8)

Solution

simplify

lo g_{64} (8)

Solution

\frac{1}{2}

+1

Decimal Notation

0.5

Solution steps

lo g_{64} (8)

Factor the number:

64 = 2^{6}

= lo g_{2^{6}} (8)

Apply log rule:

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

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

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

Factor the number:

8 = 2^{3}

= \frac{1}{6} lo g_{2} (2^{3})

Apply log rule:

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

lo g_{2} (2^{3}) = 3

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

\frac{1}{6} \cdot 3 = \frac{1}{2}

= \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is log_{64}(8) ?
The solution to log_{64}(8) is 1/2