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Popular >

simplify log_{4}(512)

Solution

simplify

lo g_{4} (512)

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

lo g_{4} (512)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (512)

Apply log rule:

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

lo g_{2^{2}} (512) = \frac{1}{2} lo g_{2} (512)

= \frac{1}{2} lo g_{2} (512)

Factor the number:

512 = 2^{9}

= \frac{1}{2} lo g_{2} (2^{9})

Apply log rule:

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

lo g_{2} (2^{9}) = 9

= \frac{1}{2} \cdot 9

\frac{1}{2} \cdot 9 = \frac{9}{2}

= \frac{9}{2}

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Frequently Asked Questions (FAQ)

What is log_{4}(512) ?
The solution to log_{4}(512) is 9/2