Regarding compound interest solve for r: 14482=9000 (1 + r/52)^364?

Question

Compound interest and logs

Answer 1

14482 = 9000 (1 + r/52)^364

Step 1: Simplify so that you have an exponential expression on one side.
14482 / 9000 = (1 + r/52)^364
1.6091 = (1 + r/52)^364

Step 2: Use logarithms to remove exponent. Remember the rule for logs: log b^a = a log b.
log 1.6091 = log (1 + r/52)^364
log 1.6091 = 364 log (1 + r/52)
(log 1.6091) / 364 = log (1 + r/52)
5.67544 * 10^-4 = log (1 + r/52)

Step 3: Use 10^x to get rid of the log, then solve to find the answer.
10^5.67544 * 10^-4 = (1 + r/52)
1.00130767 = 1 + r/52
.00130767 = r/52
52 * 1.00130767 = r
r = 0.068 = 6.8%

Check:
14482 = 9000 (1 + r/52)^364
14482 = 9000 (1.00130767)^364
14482 = 9000 (1.00130767)^364
14482 = 9000 * 1.6091
14482 = 14481.9 (check!)