please help me with the following:

Question

The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model a=3000e^0.053t When will the account be worth $5097?

Answer 1

Set 3000e^0.053t = $5097
e^0.053t = 5097/3000 = 1.699
Take the natural log of both sides
.053 t = 0.53
t = _?_ years

Answer 2

I got 10 years, but my answer choices are: a. 2010, b.2011, c.2009, d. 2012.
And I don't understand how you took the natural log of both sides?

Answer 3

You add t to the year 2000 in this case, so the answer is a.
Taking the natural log (to base e) was in my case done with a hand calculator. The natural log of e^x is x.