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find_the_fun
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is \(\displaystyle e^{2 \ln{|x|}} = |x^2|\) or \(\displaystyle x^2\)?
find_the_fun said:is \(\displaystyle e^{2 \ln{|x|}} = |x^2|\) or \(\displaystyle x^2\)?
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.
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.
The correct answer is |x^2|.
You can simplify e^(2ln|x|) by using the properties of logarithms and exponents. In this case, you can rewrite it as |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.