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Popular >

simplify 2^{log_{4}(n)}

Solution

simplify

2^{l o g_{4} (n)}

Solution

n

Solution steps

2^{l o g_{4} (n)}

Factor the number:

4 = 2^{2}

= 2^{l o g_{2^{2}} (n)}

Apply log rule:

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

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

= 2^{\frac{1}{2} l o g_{2} (n)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

2^{\frac{1}{2} l o g_{2} (n)} = (2^{l o g_{2} (n)})^{\frac{1}{2}}

= (2^{l o g_{2} (n)})^{\frac{1}{2}}

Apply log rule:

a^{l o g_{a} (b)} = b

2^{l o g_{2} (n)} = n

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

Apply exponent rule:

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

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

= n

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Frequently Asked Questions (FAQ)

What is 2^{log_{4}(n)} ?
The solution to 2^{log_{4}(n)} is sqrt(n)