Council Rock School District / Overview



Common and Natural Logarithms

Name Period #

Definition 1: The logarithm with base 10 is called the ________________________ logarithm.

o The base does not need to be shown when writing a common logarithm.

o “log x” is understood to mean “log10x”. (You do not have to write the 10).

o The LOG key on your calculator gives base 10 logarithms.

Ex 1: Evaluate log 8 log108 = y 10y = 8 (This is why we need our calculator!)

Evaluate the common logarithms using your calculator. Round to the nearest hundredth.

2) log 5 3) log 10 4) log 9.5

Definition 2: The logarithm with base e is called the _________________________ logarithm.

o Written in the form logex or ln x. (They both have the same meaning)

Ex 5: Evaluate loge9 loge9 = y ey = 9 (This is why we need our calculator!)

Ex 6: Evaluate ln 15 loge15 = y ey = 15 (This is why we need our calculator!)

Evaluate the natural logarithms using your calculator. Round to the nearest hundredth.

7) ln 0.1 8) ln 0.25 9) loge4

Common and Natural Logs Practice Worksheet

Name Period #

Evaluate the common logarithms using your calculator. Round to the nearest hundredth.

1) log 9 2) log 22 3) log 6.25 4) log 1

Evaluate the natural logarithms using your calculator. Round to the nearest hundredth.

5) loge5 6) ln 0.46 7) loge[pic] 8) ln 7

Evaluate the logarithms. DO NOT USE YOUR CALCULATOR!

9) log4256 = 10) log3243 = 11) [pic] =

12) [pic]= 13) [pic] = 14) [pic] =

Solve.

15) log6x = 4 16) log0.2x = 3 17) logx216 = 3

18) [pic] 19) [pic] 20) [pic]

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