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Popular >

simplify log_{4}(2sqrt(2))

Solution

simplify

lo g_{4} (22)

Solution

\frac{3}{4}

+1

Decimal Notation

0.75

Solution steps

lo g_{4} (22)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (22)

Apply log rule:

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

lo g_{2^{2}} (22) = \frac{1}{2} lo g_{2} (22)

= \frac{1}{2} lo g_{2} (22)

22 = 2^{\frac{3}{2}}

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

Apply log rule:

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

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

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

\frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4}

= \frac{3}{4}

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Frequently Asked Questions (FAQ)

What is log_{4}(2sqrt(2)) ?
The solution to log_{4}(2sqrt(2)) is 3/4