Solving logarithmic equation for n I have the following equation and I am trying to isolate n: 8n^2 = 64 n log_2 n Haven't done algebra in years and can't figure out how to get rid of the log_2
Simone Watts
Answered question
2022-11-05
Solving logarithmic equation for
Haven't done algebra in years and can't figure out how to get rid of the .
Answer & Explanation
Jackson Trevino
Beginner2022-11-06Added 14 answers
As said in comments, because of the logarithm, ; so, as you wrote, the equation simplifies to
which does not have a solution in terms of elementary functions. However, any equation which can be written as
has a solution which is expressed in terms of the Lambert function. In your case, there are two solutions given by
If you do not want (or cannot) to use Lambert function, you could use a root-finding method such as Newton. Starting with a "reasonable" guess , this will find the solution of
updating the guess according to
For your case, the iterative schme will then be
Let us start with a very poor estimate such as ; Newton successive iterates will then be , , , which is the solution for six significant figures.