Unit 11, Part 2:
Logarithms, Day 2
Evaluating
Logarithms
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 1.5315 rounded to 4 decimal
places.
• (This means that 10^1.5315 is approximately 34.)
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 2.718.
• 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 3.5264 rounded to 4 decimal
places.
• (That means that e^3.5264 is approximately 34.)
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.
• 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 3.8074
Evaluate the following to 4 decimal places.
1) log 76
2) log 0.43
… 1.8808
3) ln 76
… –0.3665
4) ln 0.43
… 4.3307
… –0.8440
5) log4 56
… log(56)/log(4) … 2.9037
6) log0.3 76
… log(76)/log(0.3) … –3.5970
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 = 56
2) logx+1 (34) = 13
3) log7 (3x – 2) = 128
4) w(x – 3) = 6y
Use your calculator to evaluate the following log values to 4 decimal
places.
5) log 54
6) log 0.64
7)
8) log6 1.45
log4 87
9) ln 78
10) ln 1.26