When platinum-197 undergoes a nuclear decay it becomes gold-197. The half life of platinum-197 is 20 h

a) how long would it take to turn 90% of a 1kg of platinum-197 into gold.

My answer:

0.90=1(0.5)^(t/20)

0.90/1=0.5^(t/20) log of both sides

log 0.90=t/20 log0.5

(log 0.90/log0.5)*20=t

3.04 hours=t

answer in my book is 66.4 hours! what am i doing wrong! Thanks in advance!