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Popular >

simplify log_{4}(sqrt(2))

Solution

simplify

lo g_{4} (2)

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

lo g_{4} (2)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

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

Apply log rule:

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

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

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

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

= \frac{1}{4}

Popular Examples

simplify (2+3i)^3 simplify

(2 + 3 i)^{3}

3(2x-1)-(4x+1)-2(5x-6)<= 8

3 (2 x - 1) - (4 x + 1) - 2 (5 x - 6) \leq 8

∣ 2 x - 4 ∣ \leq - x + 3

n^{2} + 2 n + 4 = 0

4 x^{2} = 60

Frequently Asked Questions (FAQ)

What is log_{4}(sqrt(2)) ?
The solution to log_{4}(sqrt(2)) is 1/4