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

In summary, e^(2ln|x|) is a mathematical expression representing the natural exponential function raised to the power of 2 times the natural logarithm of the absolute value of x. The difference between |x^2| and x^2 is that |x^2| is always positive while x^2 can be positive or negative. The correct answer for e^(2ln|x|) is |x^2|. To simplify e^(2ln|x|), you can use the properties of logarithms and exponents to rewrite it as |x^2|. It is not possible for e^(2ln|x|) to be equal to x^2 because |x^2| is always positive while x^2 can
  • #1
find_the_fun
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is \(\displaystyle e^{2 \ln{|x|}} = |x^2|\) or \(\displaystyle x^2\)?
 
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  • #2
find_the_fun said:
is \(\displaystyle e^{2 \ln{|x|}} = |x^2|\) or \(\displaystyle x^2\)?

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

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

What is e^(2ln|x|)?

e^(2ln|x|) is a mathematical expression that represents the natural exponential function raised to the power of 2 times the natural logarithm of the absolute value of x.

What is the difference between |x^2| and x^2?

The absolute value of x^2, or |x^2|, is always positive. On the other hand, x^2 can be either positive or negative, depending on the value of x.

Which one is the correct answer, e^(2ln|x|) = |x^2| or x^2?

The correct answer is |x^2|.

How do you simplify e^(2ln|x|)?

You can simplify e^(2ln|x|) by using the properties of logarithms and exponents. In this case, you can rewrite it as |x^2|.

Can e^(2ln|x|) ever be equal to x^2?

No, e^(2ln|x|) cannot be equal to x^2. This is because the absolute value of x^2, or |x^2|, will always be positive while x^2 can be either positive or negative.

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