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