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

find_the_fun · 2015-02-04T09:10:08+00:00

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

MHB
Thread starter find_the_fun
Start date Feb 4, 2015
Tags

Absolute Absolute value Base Ln Natural Value

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

Feb 4, 2015

find_the_fun

is $\displaystyle e^{2 \ln{|x|}} = |x^2|$ or $\displaystyle x^2$?

Mathematics news on Phys.org

Feb 4, 2015

Prove It

Gold Member

MHB

find_the_fun said:

is $\displaystyle e^{2 \ln{|x|}} = |x^2|$ or $\displaystyle x^2$?

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

1. 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.

2. 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.

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

The correct answer is |x^2|.

4. 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|.

5. 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.