What is expand e^{(ln(x)-a)^2} ?

The solution to expand e^{(ln(x)-a)^2} is e^{ln^2(x)+a^2}x^{-2a}

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expand e^{(ln(x)-a)^2}

expand

e^{(l n (x) - a)^{2}}

e^{l n^{2} (x) + a^{2}} x^{- 2 a}

Solution steps

e^{(l n (x) - a)^{2}}

(ln (x) - a)^{2} = ln^{2} (x) - 2 a ln (x) + a^{2}

= e^{l n^{2} (x) - 2 a l n (x) + a^{2}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{- 2 l n (x) a} e^{l n^{2} (x) + a^{2}}

Simplify

e^{- 2 l n (x) a} : x^{- 2 a}

= x^{- 2 a} e^{l n^{2} (x) + a^{2}}

\frac{k ^{2} ( k + 1 ) ^{2}}{4} + (k + 1)

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\frac{π}{32} \cdot ((0.051)^{4} - (0, 41)^{4})

(sin (x) + 5 cos (x))^{2}

What is expand e^{(ln(x)-a)^2} ?
The solution to expand e^{(ln(x)-a)^2} is e^{ln^2(x)+a^2}x^{-2a}