Today in Precalculus

• Go over homework

• Notes: Common and Natural Logarithms

• Homework

Common Logs

• Base 10 is known as the common log, if no base is written in a log, it is assumed to be base 10

example: x = log 5 is the same as x = log105

• This is one of two bases we can use our calculators

• Example: x = log 260

= 2.415

Properties of Common Logs

log10=1 since 101 = 10

log10x=x since 10x = 10x

log1=0 since 100 = 1

10logx = x since logx = logx

Solving simple equations with Common Logs

Solve:

10x = 3.7

x=log3.7

x= 0.568

Solve:

logx = –1.6

x =10-1.6

x= 0.025

Natural logs• Used for the natural base, e, and can also be

calculated with calculators.

• Inverse of ex

• Abbreviated ln

• Example: x = ln14.32

= 2.662

Properties of Natural Logs

lne=1 since e1 = e

lnex=x since ex = ex

ln1=0 since e0 = 1

elnx = x since lnx = lnx

Solving simple equations with Natural Logs

Solve:

lnx = 3.45

x=e3.45

x=31.500

Solve:

ex = 6.18

x = ln6.18

x= 1.821

Homework

• Page 308: 7-35 odd