Given the equation below, how do I find the value of b so that the function is equal to 21. I tried solve but I keep getting an error message.
(15 Sqrt[π] (Erf[11 Sqrt[b]] + Erf[17 Sqrt[b]]))/(14 Sqrt[b]) == 21
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3 Answers
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You can use Solve, if you specify constraint on b
eq = (15 Sqrt[\[Pi]] (Erf[11 Sqrt[b]] + Erf[17 Sqrt[b]]))/(14 Sqrt[b]) == 21;
Solve[eq && 0 < b < 100, b]
N[%]
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First there is a typo in your equation, it should be Sqrt[Pi] and not Sqrt[[Pi]]. This equation can not solved via NSolve, but you get a result (approx 0.0325) via FindRoot:
FindRoot[(15 Sqrt[Pi] (Erf[11 Sqrt[b]] + Erf[17 Sqrt[b]]))/(14 Sqrt[
b]) - 21, {b, 1.}]
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$\begingroup$ I do not believe that
Sqrt[\[Pi]]is incorrect. $\endgroup$ Mar 8, 2015 at 19:11 -
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You can use FindInstance to find one solution:
N@FindInstance[(15 Sqrt[Pi] (Erf[11 Sqrt[b]] + Erf[17 Sqrt[b]]))/(14 Sqrt[b]) == 21, {b}]
{{b -> 0.0325472}}
