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Popular >

simplify (e^x)^{ln(x)}

Solution

simplify

(e^{x})^{l n (x)}

Solution

x^{x}

Solution steps

(e^{x})^{l n (x)}

Apply exponent rule:

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

= e^{x l n (x)}

Apply exponent rule:

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

= (e^{l n (x)})^{x}

Apply log rule:

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

e^{l n (x)} = x

= x^{x}

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Frequently Asked Questions (FAQ)

What is (e^x)^{ln(x)} ?
The solution to (e^x)^{ln(x)} is x^x