I want to simplify the following expression. \(\displaystyle{Y}=\text{Bottom}+{\frac{{\text{Top}-\text{Bottom}}}{{{1}+{10}^{{{\left({\left({\log{{E}}}{C}{50}-{X}\right)}\right)}}}}}}\) log

Jefferson Pacheco

Jefferson Pacheco

Answered question

2022-04-09

I want to simplify the following expression.
Y=Bottom+TopBottom1+10((logEC50X))
log is base of 10. Some may know that it's a dose response curve, and I want to solve for EC50.
I tried simplifying it but I forgot math long time ago and I couldn't find the answer online.
My problem was the exponential and logarithms part.
Can someone simplify the expression to solve for EC50?
Thank you very much.
Edit : And if someone could explain simplifying exponential and logarithm on this one, it would be great as well. I forgot all the math and I would appreciate it.

Answer & Explanation

tabuevniru8op

tabuevniru8op

Beginner2022-04-10Added 14 answers

Starting with
Y=Bottom+TopBottom1+10log10EC50X
then using 10log10EC50X=EC5010X (if that is what you meant) you get
YBottom=TopBottom1+EC5010X
or
1+EC5010X=TopBottomYBottom
i.e
EC50=10XTopYYBottom.

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