Question 1016228: How do you evaluate log base 3 of 100 without using a calculator?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Well you cannot get an exact value...you can start to estimate by looking at the equivalent exponential expression:
3^x = 100
We know 3^4 = 81 and 3^5 = 243 and we can interpolate to get an estimate...we can also use differentials to get an estimate but getting an exact value is impossible...
Thus a fair starting estimate is about 4 19/142, or about 4.15...
We can solve the above as well and get
x log 3 = log 100
x = 2 /.48 = 4.167 which is a bit better...
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