Evaluate log3 (1/3)

Question

Evaluate log3 (1/3). (The number right after the log, which is 3, is the base)

Answer 1

Note that log_aa=1 (a ≠1,0) since a^1=a.

 

Also, logaⁿ=nloga (for any base).

 

Since 1/3=3^-1, log₃(1/3)=log₃3^-1=-1*log₃3=-1

Answer 2

log_b(y) = x  --->  b^x = y

 

So we can re-write log₃(1/3) as 3^x = 1/3  -->  x = -1