Table of Contents

Logarithm Properties - Product Rule

• The Product Rule for logarithms states that ...

NlogMlog)NM(log bbb read as “the log of the product is the sum of the logs.”

• Example 1:

2.9log7log)2.97(log 333

• Example 2:

)17410(log174log10log 555

Table of Contents Slide 2

Logarithm Properties - Product Rule

• Example 3:

Show that log 30 is equivalent in value to log 3 + log 10.

The product rule states that ...

10log3log)103log(30log

log 30 = ...

and log 3 + log 10 = ...

... which are the same.

Table of Contents Slide 3

Logarithm Properties - Product Rule

• Example 4:

Show that ln 48 is equivalent in value to ln 4 + ln 12.

The product rule states that ...

12ln4ln)124ln(48ln

ln 48 = ...

and ln4 + ln 12 = ...

... which are the same.

Table of Contents

Logarithm Properties - Product Rule