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