The document discusses natural logarithms (ln) and their properties. It notes that ln e = 1, and that all logarithm laws still apply when using natural logs, such as ln(M × N) = lnM + lnN. It suggests using natural logs may be easier than common logs in some cases. It then provides examples of using natural logs to model continuous growth and radioactive decay.

1. Estimate the value of log535. Justify your answer.
Claire correctly solves the following equation:
log2(6 - x) + log2(3 - x) = 2
She finds two possible values of x: x = 2 and x = 7.
Identify which one of these values is unacceptable and explain why.
Identify which one of the following questions would be non-calculator
and explain why.
8x-3 = 1 10x = -42x - 1
32
1.
2.
3.

2. Natural Logs
Recall, log is called a "common log" ie. log
How about, called the natural log
Note, ln e = 1
e
All log laws still apply
ex. ln(M · N) = lnM + lnN
Could use log or ln
Where to use ln?
again could use log or ln *ln easier

4. Ex) The population of a certain country is 28 million
and grows continuously at a rate of 3% annually.
How many years will it take for the population to reach
40 million?
Continuous Growth + Decay Problems
A = Pert

5. Ex) A radioactive substance decays so that the
amount present is "P" grams after "t" years according
to the following: P = 50e-0.135t. What is the half life of
the substance?
Half life = the amount of time it takes for the substance
to decay to half its original amount.