Unformatted text preview: a,b ) has a smaller length than 1 2 . (How small can you make it? Can you evaluate L (30) exactly?) 5. Use the same ideas to estimate L (50) (ie, ﬁnd a < b and prove L (50) ∈ ( a,b ), with b-a as small as you like; be as precise or as rough as you want). Remarks The base-10 logarithm function log x satisﬁes properties like (1), (2), (3). In precalculus it is likely that (1), (2), (3) (and their consequences, like Exercises 1-3) were all you knew about the logarithm. You might wonder: is there more than one function with these properties? (What would the others be? Why are they less important than log x ?) If there is only one function with these properties, we should be able to use (1), (2), (3) and nothing else to calculate logarithms to any degree of precision. (Does your experience with 4 and 5 suggest this is possible?)...
View Full Document
- Fall '07
- Math, Natural logarithm, Logarithm, Common logarithm, base-10 logarithm function