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Popular >

expand e^{2(ln|x|+C)}

Solution

expand

e^{2 (l n ∣ x ∣ + C)}

Solution

e^{2 C} x^{2}

Solution steps

e^{2 (l n ∣ x ∣ + C)}

Expand

2 (ln ∣ x ∣ + C) : 2 ln ∣ x ∣ + 2 C

= e^{2 l n ∣ x ∣ + 2 C}

Apply exponent rule:

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

= e^{2 l n ∣ x ∣} e^{2 C}

Simplify

e^{2 l n ∣ x ∣} : ∣ x ∣^{2}

= ∣ x ∣^{2} e^{2 C}

Apply absolute rule:

∣ x ∣^{2} = x^{2}

, assuming

x \in R

∣ x ∣^{2} = x^{2}

= x^{2} e^{2 C}

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Frequently Asked Questions (FAQ)

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