Find the solution to the equation, \( 2 e^{3 y+8}-11 e^{5-10 y}=0 \) (correct to 4 decimal places) \( \} \mathrm{y}= \)

Solve the equation \( 2e^(3y+8)-11e^(5-10y)=0 \). Solve the equation by following steps: - step0: Solve for \(y\): \(2e^{3y+8}-11e^{5-10y}=0\) - step1: Factor the expression: \(e^{5}\left(2e^{3}\times e^{13y}-11\right)\left(e^{y}\right)^{-10}=0\) - step2: Rewrite the expression: \(\frac{2e^{13y+8}-11e^{5}}{\left(e^{y}\right)^{10}}=0\) - step3: Cross multiply: \(2e^{13y+8}-11e^{5}=\left(e^{y}\right)^{10}\times 0\) - step4: Simplify the equation: \(2e^{13y+8}-11e^{5}=0\) - step5: Rewrite the expression: \(2e^{13y+8}=11e^{5}\) - step6: Divide both sides: \(\frac{2e^{13y+8}}{2}=\frac{11e^{5}}{2}\) - step7: Divide the numbers: \(e^{13y+8}=\frac{11e^{5}}{2}\) - step8: Take the logarithm of both sides: \(\ln{\left(e^{13y+8}\right)}=\ln{\left(\frac{11e^{5}}{2}\right)}\) - step9: Evaluate the logarithm: \(13y+8=\ln{\left(\frac{11e^{5}}{2}\right)}\) - step10: Move the constant to the right side: \(13y=\ln{\left(\frac{11e^{5}}{2}\right)}-8\) - step11: Divide both sides: \(\frac{13y}{13}=\frac{\ln{\left(\frac{11e^{5}}{2}\right)}-8}{13}\) - step12: Divide the numbers: \(y=\frac{\ln{\left(\frac{11e^{5}}{2}\right)}-8}{13}\) - step13: Simplify: \(y=\frac{\ln{\left(11\right)}-3-\ln{\left(2\right)}}{13}\) - step14: Simplify: \(y=\frac{\ln{\left(\frac{11}{2}\right)}-3}{13}\) - step15: Evaluate: \(y=\frac{\ln{\left(11\right)}-\ln{\left(2\right)}-3}{13}\) The solution to the equation \(2e^{3y+8}-11e^{5-10y}=0\) is \(y \approx -0.099635\) (correct to 4 decimal places).