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Popular >

simplify sqrt(2)^{log_{2}(x)}

Solution

simplify

2^{l o g_{2} (x)}

Solution

x

Solution steps

(2)^{l o g_{2} (x)}

Apply radical rule:

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

Simplify

\frac{1}{2} lo g_{2} (x) : \frac{lo g _{2} ( x )}{2}

= 2^{\frac{l o g _{2} ( x )}{2}}

Simplify

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

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

Apply exponent rule:

a^{b c} = (a^{b})^{c}

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

Apply log rule:

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

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

= x

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Frequently Asked Questions (FAQ)

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