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Popular >

simplify log_{4}(sqrt(1024))

Solution

simplify

lo g_{4} (1024)

Solution

\frac{5}{2}

+1

Decimal Notation

2.5

Solution steps

lo g_{4} (1024)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (1024)

Apply log rule:

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

lo g_{2^{2}} (1024) = \frac{1}{2} lo g_{2} (1024)

= \frac{1}{2} lo g_{2} (1024)

1024 = 2^{5}

= \frac{1}{2} lo g_{2} (2^{5})

Apply log rule:

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

lo g_{2} (2^{5}) = 5

= \frac{1}{2} \cdot 5

\frac{1}{2} \cdot 5 = \frac{5}{2}

= \frac{5}{2}

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Frequently Asked Questions (FAQ)

What is log_{4}(sqrt(1024)) ?
The solution to log_{4}(sqrt(1024)) is 5/2