We will solve for x using the very basic properties of natural logarithms. I'll illustrate it below. Explanation: We have, ln ( x − 2 ) 2 = 6 Using the property, ln m n = n ln m , We have, ln ( x − 2 ) 2 = 6 ⇒ 2 ln ( x − 2 ) = 6
⇒ ln ( x − 2 ) = 3
⇒ x − 2 = e 3 In the last step, we used the concept of inverse of the natural logarithms, ln m = n ⇒ m = e n Thus, x = e 3 + 2 Where e is the base of natural logarithms.