when does g(x)=e^3x - 70 equal 0?

It's where e^(3x) = 70

Take the natural log of both sides

 Ln e^(3x) =  Ln 70     And by  a property of logs, the left side just becomes 3x...so we have..

3x = Ln 70                  Divide both sides by 3

x =  Ln70 / 3    ≈ 1.416