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"mixed" logarithmic equation
I'm trying to solve for x in the following equation: e^(-66/x)/x^2 = c, where c is a constant
By taking ln of both sides and then dividing by 2, I get to:
-33/x -ln(x) = c/2
Then, in order to get an approximate answer, I tried substituting e with its approximation up to a few decimal places, in the original problem statement, but that didn't get me far. I'm considering doing a Taylor series approximation for the 'ln(x)' term (i.e (x-1) - (x-1)^2 + (x-1)^3)) and then solving for x. Is there an easier and/or more precise and/or more direct way? Note, I understand that the taylor approximation I used is meant for x, such that |x| is at most 1. This is why I only went with 3 terms.
Homework Statement
I'm trying to solve for x in the following equation: e^(-66/x)/x^2 = c, where c is a constant
Homework Equations
The Attempt at a Solution
By taking ln of both sides and then dividing by 2, I get to:
-33/x -ln(x) = c/2
Then, in order to get an approximate answer, I tried substituting e with its approximation up to a few decimal places, in the original problem statement, but that didn't get me far. I'm considering doing a Taylor series approximation for the 'ln(x)' term (i.e (x-1) - (x-1)^2 + (x-1)^3)) and then solving for x. Is there an easier and/or more precise and/or more direct way? Note, I understand that the taylor approximation I used is meant for x, such that |x| is at most 1. This is why I only went with 3 terms.
Homework Statement
Homework Equations
The Attempt at a Solution
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