SOLUTION: How do you find the log of a number to any base, we can use a conversion formula log b^a = log a ______ log b Using this formaul, how do I find log 2 10

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do you find the log of a number to any base, we can use a conversion formula log b^a = log a ______ log b Using this formaul, how do I find log 2 10      Log On


   

Question 73437: How do you find the log of a number to any base, we can use a conversion formula
log b^a = log a
______
log b
Using this formaul, how do I find log 2 1000. Round to the hundredth's place.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To evaluate a log that doesn't have a base of 10, you would use the change of base formula
log_%5Bb%5D%28a%29=%28log%28a%29%29%2F%28log%28b%29%29Where the logs on the right are logs of base 10. So if I have
log_%5B2%5D%281000%29 It would look like this with the change of base formula
log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29
So if we evaluate log(1000) we get 3 (10^3=1000) and if we evaluate log(2) we get 0.30103 approximately
So
log_%5B2%5D%281000%29=%28log%281000%29%29%2F%28log%282%29%29=3%2F0.30103=9.96578Approximately
So log_%5B2%5D%281000%29 (or the log base 2 of 1000) is approximately equal to 9.96578
Check:
2%5Ex=1000If we plug in 9.96578 for x we should get 1000
2%5E%289.96578%29=1000
999.99999=1000 Which is very close to true, since we have round off errors this is good enough.
Hope this makes sense.