MHB Does e^{2 \ln{|x|}} = |x^2| or x^2?

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The equation e^{2 ln{|x|}} simplifies to x^2, as the natural logarithm and exponential functions cancel each other out. The expression |x^2| is equivalent to x^2 since squaring any real number results in a non-negative value. Therefore, both e^{2 ln{|x|}} and |x^2| yield the same result, confirming their equality. This demonstrates the properties of logarithms and exponents in relation to absolute values. Ultimately, e^{2 ln{|x|}} is equal to x^2.
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is [math]e^{2 \ln{|x|}} = |x^2|[/math] or [math]x^2[/math]?
 
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find_the_fun said:
is [math]e^{2 \ln{|x|}} = |x^2|[/math] or [math]x^2[/math]?

Both, since squaring makes everything non-negative anyway...
 

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