I need help with netwon method

Question

Use Newton's method to approximate the indicated solution of the equation correct to six decimal places.

the positive solution of e^3x = x + 8

Answer 1

e^3x - x - 8 = 0; x₀ = 0.5; f'(x) = 3e^3x - 1; x_n+1 = x_n - f(x_n)/f'(x_n) = x_n - (e^3x - x - 80.822)/(3e^3x - 1);

x₁ = 0.822884;

x₂ = 0.736200

x₃ = 0722259

x₄ = 0.721948

x₅ = 0.721948