SOLUTION: find the exact value of the logarithm without using a calculator: log3 (1/81)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: find the exact value of the logarithm without using a calculator: log3 (1/81)      Log On


   

Question 605869: find the exact value of the logarithm without using a calculator:
log3 (1/81)
Found 2 solutions by htmentor, MathTherapy:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Since 81 = 3^4, we can write the expression as
log3(1/3^4) = log3(1) - log3(3^4) = 0 - 4*log3(3) = -4

Answer by MathTherapy(10862) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact value of the logarithm without using a calculator: log3 (1/81)
***************
log+%283%2C+%281%2F81%29%29
log+%283%2C+%281%2F3%5E%284%29%29%29 --- Converting 81 to 3%5E4
log+%283%2C+%283%29%5E%28-+4%29%29 --- Converting 1%2F3%5E4 to 3%5E%28-+4%29
              - 4 ----- Applying log+%28b%2C+%28b%5Ec%29%29+=+c