How can I solve this nature log equation? ln(x+2)=e^((x-4)) Is there any way to solve this equation without graphing or using GDC ?
omvamen71
Answered question
2022-09-03
How can I solve this nature log equation?
Is there any way to solve this equation without graphing or using GDC ? Thank you
Answer & Explanation
Quinn Alvarez
Beginner2022-09-04Added 13 answers
The presence of two layers of exponentials does not give any hope for analytical solutions and numerical methods are required. Consider
The first derivative cancels for
( being Lambert function); at this point
On the other side, by inspection, is a small positive number; the second derivative being always positive, there are two roots on each side of . Let us use Newton method. For the first root, let us select ; the successive iterates will then be
which is the solution for fifteen significant digits. For the second root, let select (twice the value of ); the successive iterates will then be
which is the solution for fifteen significant digits.