1. Unit 11, Part 2: Logarithms, Day 2 Evaluating Logarithms

2. Common Log
There are two buttons on your calculator that evaluate logs. The LOG button and the LN button.
The LOG button is used to evaluate logarithms of base 10. It is called the “common log.” If a log does not have a designated base, it is “understood” to be a base 10 or common log.
To evaluate the log 34, hit the LOG button and type in 34… We usually round log values to 4 decimal places… Its value is approximately rounded to 4 decimal places.
(This means that 10^ is approximately 34.)

3. Natural Log
The LN button is used to evaluate logarithms of base “e”. It is called the “natural log.” If a log is written as “ln”, it is “understood” to be a base e or natural log.
“e” is similar to “pi” in that it is an irrational number and has a set value. Where as pi is rounded to 3.14, e is rounded to
To evaluate the ln 34, hit the LN button and type in 34… We usually round log values to 4 decimal places… Its value is approximately rounded to 4 decimal places.
(That means that e^ is approximately 34.)

4. Logarithms of Other Bases
The calculator will not automatically evaluate logs of other bases. You have to “change the base.”
The CHANGE OF BASE formula allows you to change a logarithm into any base that is needed!
logb x = loga (x) / loga (b)
(A log is turned into the division of the log of the value by the log of the base, with the new or desired base on the logs.)
Usually we turn logs into base 10 [LOG] so we can use the calculator to evaluate them.

5. If we convert it into base 10, we can evaluate it with the calculator…
So the expression in base 2 can be turned into an equivalent expression in any base that we need!
log2 14 can be turned into log3 (14)/log3 (2)… in base 3
log2 14 can be turned into log5 (14)/log5 (2)… in base 5
log2 14 can be turned into log (14)/log (2)… in base 10
If we convert it into base 10, we can evaluate it with the calculator…
log2 14 = log (14)/log (2) which is about

6. Evaluate the following to 4 decimal places.
log ) log 0.43
… … –0.3665
3) ln ) ln 0.43
… … –0.8440
log4 56
… log(56)/log(4) …
log0.3 76
… log(76)/log(0.3) … –3.5970

7. Intro to Logs Practice:
Write the form given. Identify it as “Log Form” or “Exponential Form” and then convert it to the other form.
1) 5x = ) logx+1 (34) = 13
3) log7 (3x – 2) = ) w(x – 3) = 6y
Use your calculator to evaluate the following log values to 4 decimal places.
5) log ) log 0.64
log ) log
9) ln ) ln 1.26