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Warm up Problems
1.
2. At higher elevations, water takes longer to boil. Let f (h) be the boiling point, in ºC, at altitude h meters above sea level. Using correct units, explain the meaning of 1 90 3000f
101
lim5.2xx
x
Logarithmslog y
a x y a x ln logex x
Laws of Logarithms
ln ln lnAB A B
ln ln lnA
A BB
ln lnnA n A
log xa a x
loga xa x
ln1 0
Ex. Express as a single logarithm
2log 3log logx y z
Pract. Simplify2
2 1
log 2log
log log AB
A B
A
Ex. Solve 20 2 50 1.04x x
Ex. Solve 10 7x xe
Ex. The half-life of a substance is 12 days. If there are 10.32g initially, write an equation that represents the amount, A, of the substance after t days. When will there be 1g left?
Note: Logarithmic functions are always dominated by increasing power functions.
“n to the n” FEPLLnn
Factorial
Exponent
Polynomial
Linear
Logarithm
grows faster
grows slower
as x
Ex. Define
a) Is g increasing or decreasing?
b) Explain why g is invertible and find g -1.
2
5xg x
e