Ln 4 r^2 =3

To find the value of r in the equation ln(4r^2) = 3, we can solve for r by using exponential properties and the definition of the natural logarithm.

Step 1: Rewrite the equation using the definition of the natural logarithm:
4r^2 = e^3

Step 2: Divide both sides of the equation by 4 to isolate r^2:
r^2 = e^3 / 4

Step 3: Take the square root of both sides to solve for r:
r = √(e^3 / 4)

Step 4: Simplify the expression under the square root:
r = √(e^3) / √(4)

Step 5: Simplify the square root of 4:
r = √(e^3) / 2

Thus, the solution for r in the equation ln(4r^2) = 3 is r = √(e^3) / 2.