Answer:
x = -0.23
Step-by-step explanation:
2000=5000e^4x
=> e^4x = 2000/5000 = 2/5
taking the natural logarithn on LHS and RHS
ln e^4x = ln2/5
=> 4x lne = ln2/5
we know ln e = 1, also ln a/b = lna - ln b
ln 2 = 0.693, ln 5 = 1.609
4x = ln2 - ln5
4x = 0.693 - 1.609
x = -0.916/4 = -0.229
Thus, x = -0.23 rounded to two decimal place.
