Solving for log function

Hi all,

I'm new to MATLAB and need help in solving for a in the following equation:

ln(1/R_1)^a - ln(1/R_2)^a = 0

My script already calculates for R_1 and R_2; I just need a, and I need to do it without taking the log of a log. Any help would be appreciated!

Answer 1

[Matt Fig]

Use the FZERO function. What values do you have for R_1 and R_2?

F = @(a) log(1/R_1).^a - log(1/R_2).^a
rt = fzero(F,.1);

Answer 2

[Walter Roberson]

Within those constraints, the solution is:

a = 0

The more general solution is

a = -(2*I)*Pi*T/(ln(ln(1/R_1))-ln(ln(1/R_2)))

where I is sqrt(-1) and T is every arbitrary integer. However, that solution requires taking the log of a log and is thus ruled out by the question.

There are no other non-trivial solutions.

If you were able to assign a range of values to R_1 and R_2 and a required accuracy, then there might be a series or taylor expansion that was able to find the basic solution to within the desired accuracy without using logs of logs.

[Walter Roberson]

Even if you know R_2 then tayloring would not work within the confines of the question, as the taylor expansion requires taking the log(log(R_2)) at least once, violating the constraint that *no* log of log can be taken.