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Unformatted text preview: erence of logarithms and so we can write
it as a single logarithm with a quotient. æ ( x + y )5 ö
5ln ( x + y ) - 2 ln y - 8ln x = ln ç 2 8 ÷
ç yx ÷
[Return to Problems] The final topic that we need to discuss in this section is the change of base formula.
Most calculators these days are capable of evaluating common logarithms and natural logarithms.
However, that is about it, so what do we do if we need to evaluate another logarithm that can’t be
done easily as we did in the first set of examples that we looked at?
To do this we have the change of base formula. Here is the change of base formula. log a x = log b x
logb a where we can choose b to be anything we want it to be. In order to use this to help us evaluate
logarithms this is usually the common or natural logarithm. Here is the change of base formula
using both the common logarithm and the natural logarithm. log a x = log x
log a log a x = ln x
ln a Let’s see how this works with an example. Example 6 Evaluate log 5 7 .
First, notice that we can’t use the same method to do this eva...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12