If (e^x)^-2 X (e^x)^2 X e^x = 1/e^2
find x?
I have no idea how to do this
(e^x)^-2=1/(e^x)^2
(e^x)^-2*(e^x)^2*e^x=[1/(e^x)^2]*[(e^x)^2]*e^x=1/e^2
[1/(e^x)^2]*[(e^x)^2]=1
1*e^x=1/e^2
e^x=e^-2
ln(e^x)=ln(e^-2)
ln(e^x)=x
ln(e^-2)= -2
x= -2
Thank You so much!!
To solve this equation, we can simplify the left side by using the properties of exponents.
Step 1: Simplify the left side using the rule (a^m)^n = a^(m*n):
((e^x)^-2) * ((e^x)^2) * e^x
= (e^(-2x)) * (e^(2x)) * e^x
= e^(-2x + 2x + x)
= e^x
Step 2: Set the simplified left side equal to the right side and solve for x:
e^x = 1/e^2
We can rewrite 1/e^2 as e^(-2).
So, e^x = e^(-2)
Since the bases (e) are equal, the exponents must be equal. Therefore:
x = -2
So, x = -2 is the solution to the equation.