e^(ln2x)=e^2 (?)

Question

e^(ln2x)=e^2 (?)

thanks in advance

Answer 1

so ln(2x) = 2

e^2 = 2x
x = e^2/2

Answer 2

To determine whether the equation e^(ln(2x)) = e^2 is true, we can simplify both sides of the equation using the properties of logarithms and exponents.

Let's start with the left side of the equation: e^(ln(2x)). The property of logarithms states that e^(ln(x)) = x.

Applying this property to the equation, we have: e^(ln(2x)) = 2x.

So, the left side of the equation simplifies to 2x.

Next, let's simplify the right side of the equation: e^2. The value of e^2 is a constant, approximately equal to 7.389.

Now, we can rewrite the simplified equation: 2x = 7.389.

To solve for x, we divide both sides of the equation by 2: x = 7.389/2.

Therefore, the solution to the equation e^(ln(2x)) = e^2 is x ≈ 3.6945.

So, the equation is not true, as it only holds for x ≈ 3.6945, and not for all values of x.

e^(ln2x)=e^2 (?)

so ln(2x) = 2

cheers

To determine whether the equation e^(ln(2x)) = e^2 is true, we can simplify both sides of the equation using the properties of logarithms and exponents.