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The Natural logarithm and e
IB SL/HL Adrian Sparrow
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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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Using the natural log - ln
Without using a calculator find the value of: 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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Remember the base of a natural log is e.
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:
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