Unit 11, Part 2: Logarithms, Day 2 Evaluating Logarithms.
Transcript of Unit 11, Part 2: Logarithms, Day 2 Evaluating Logarithms.
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. It’s value is approximately 1.5315 rounded to 4 decimal places.
• This means that 101.5315 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. Whereas 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. It’s value is approximately 3.5264 rounded to 4 decimal places.
• That means that e3.5264 is approximately 34.
Logarithms of Other Bases
• The LOG key does not allow you to input a different base. You have to change the base to 10.
The CHANGE OF BASE formula allows you to change a logarithm into any base that is needed!
logb x = loga (x) / loga (b)
Usually we turn logs into base 10 so we can use the calculator to evaluate them.
• So an 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 … –0.3665
3) ln 76 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
Warmup: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) log4 87 8) log6 1.45
9) ln 78 10) ln 1.26