For m in Q=log(m)(m−1/m). The domain of m is ]0,infty[. For a given Q, whenever I find a m=m∗ satisfying the equality, the equality is also satisfied with m=1/m∗. Therefore, I can limit the domain of m to ]1,infty[.

Isaac Barry

Isaac Barry

Answered question

2022-09-04

Working on a problem related to effect size, I get this relation where
Q = log ( m ) ( m 1 m )
The domain of m is ] 0 , [. For a given Q, whenever I find a m = m satisfying the equality, the equality is also satisfied with m = 1 / m . Therefore, I can limit the domain of m to ] 1 , [.
Is there a formula that can isolate m so that given a value Q ( Q R + ), m follows?

Answer & Explanation

Joel Reese

Joel Reese

Beginner2022-09-05Added 17 answers

There are only two solutions for a given Q. If you want to solve the equation using iterative method would work
m n + 1 = log ( m n ) ( m n 2 1 ) Q
Use an initial guess m 0 in ( 0 , 1 ). As this will make sure that square term doesn't explode. You can get arbitrary accuracy from this.

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