The Natural logarithm and e

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The Natural logarithm and e

• IB SL/HL
• Adrian Sparrow
• www.ibmaths.com

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Learning outcome you should be able to find
the inverse of ln(x), you should be able to
solve equations by using the relationship between
the natural logarithm and e.
Note is used to denote
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Look at the graph below - what relationship do
the two functions have?
then
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Without using a calculator find the value of
Using the natural log - ln
Use a calculator to find
3
0
4
1

2
-3

-1
n
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The laws of natural logarithms
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Finding a missing index using logarithms
Find x to 2 decimal places using trial and error.
This process can be used with any base log, even
the natural log.
Far too complicated ...
Take a log of both sides
Now try these, answers to 2 d.p.
Use the power rule
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Find x, if
Find x, if
Remember the base of a natural log is e.
Take a natural log of both sides.
Rearrange in index form.
Use the power rule.
Find x in each of the following
Find x in each of the following