Râ‹… ln ( (2â‹…16)/R )- 1050/1500 =0 , find R
You asked:
Solve the equation \[R \ln\left( \frac{2 \cdot 16}{R} \right) - \frac{1050}{1500} = 0\] for the unknown \(R\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}R &= \frac{32}{e^{- W\left(- \frac{7}{320}\right)}} \approx 31.292112\\R &= \frac{32}{e^{- W_{-1}\left(- \frac{7}{320}\right)}} \approx 0.12650971\end{aligned}\]
\(W\) is the Lambert \(W\) function, defined as the multivalued inverse function of \(f(w) = we^w\) for any complex number \(w\).
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).
\(W_{-1}\) denotes the branch of the Lambert \(W\) function that satisfies \(W(x) \le -1\) when \(x\) is real.