Rewrite the equation using the properties of logarithms:
e^ln(x+3) = e^7
Exponentiation and ln are inverse functions so the equation simplifies to:
x + 3 = e^7
Subtract 3 from both sides:
x = e^7 -3
Raise e to the power of 7 and subtract 3 from that:
x = 1093.633 ( Rounded to the nearest hundredth).