Working with logarithms I have an expression involving very small probabilities

Alisa Duarte

Alisa Duarte

Answered question

2022-03-07

Working with logarithms
I have an expression involving very small probabilities A,B,C,D.
xk1BA+k2B
xk1CD+k2C
Is there any way for me to check if x satisfies the above inequalities using log(A),log(B),log(C) and log(D)?

Answer & Explanation

teertallectutl

teertallectutl

Beginner2022-03-08Added 1 answers

You could try inverting the inequalities as follows (example, assuming k1 is positive):
1xAk1B+k2k1  or  k1xk2AB
Then taking logarithms of each side (providing LHS is positive) isolates log(A) and log(B). Not sure whether that is what you want though.

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