SOLUTION: How do you solve: 3000=2000(1+.06)^t.

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Question 22642: How do you solve: 3000=2000(1+.06)^t.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
3000=2000%281%2B.06%29%5Et

Divide both sides by 2000:
3000%2F2000+=%282000%281%2B.06%29%5Et%29%2F2000
3%2F2+=+1.06%5Et

In order to solve for t, where t is an exponent, you must take the ln of each side of the equation. It also works to take the log of each side--exactly the same answer!
ln+%283%2F2%29+=+ln+%281.06%5Et%29+

This should bring back the laws of logarithms, in which the exponent becomes the coefficient:
ln%283%2F2%29+=+t%2Aln%281.06%29+

Finally divide both sides by ln(1.06), and calculate with a calculator:
t=+%28ln%283%2F2%29%29%2F%28ln%281.06%29%29+= 6.958515, which rounds off to about 6.96.

R^2 at SCC