Step 1 :Given the equation \(\frac{581 e^{x}}{e^{x}+60}=514\)
Step 2 :First, we multiply both sides of the equation by \(e^{x}+60\) to get rid of the fraction, which gives us \(581 e^{x} = 514(e^{x}+60)\)
Step 3 :Then, we simplify the equation to get \(581 e^{x} = 514 e^{x} + 30840\)
Step 4 :Subtract \(514 e^{x}\) from both sides to get \(67 e^{x} = 30840\)
Step 5 :Divide both sides by 67 to isolate \(e^{x}\), which gives us \(e^{x} = \frac{30840}{67}\)
Step 6 :Finally, we take the natural logarithm of both sides to solve for x, which gives us \(x = \ln\left(\frac{30840}{67}\right)\)
Step 7 :\(\boxed{x = \ln\left(\frac{30840}{67}\right)}\) is the solution to the equation