SOLUTION: simplify the expression log3[1/27]^4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: simplify the expression log3[1/27]^4      Log On


   

Question 744788: simplify the expression log3[1/27]^4
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
The strategy here is to rewrite everything in terms of powers of 3 and then use the inverse property of logs:
log3%281%2F27%29%5E4=log3%28%281%2F3%5E3%29%29%5E4

log3%28%281%2F3%5E3%29%29%5E4=log3%28%283%5E%28-3%29%29%29%5E4

log3%28%283%5E%28-3%29%29%29%5E4=-12%2Alog3%283%29=-12