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. It’s value is approximately 1.5315 rounded to 4 decimal places. This means that 10 1.5315 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. 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 e 3.5264 is approximately 34.

4. 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! log b x = log a (x) / log a (b) Usually we turn logs into base 10 so we can use the calculator to evaluate them.

5. So an expression in base 2 can be turned into an equivalent expression in any base that we need! log 2 14 can be turned into log 3 (14)/log 3 (2)… in base 3 log 2 14 can be turned into log 5 (14)/log 5 (2)… in base 5 log 2 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… log 2 14 = log (14)/log (2) which is about 3.8074

6. Evaluate the following to 4 decimal places. 1)log 762) log 0.43 … 1.8808… –0.3665 3) ln 764) ln 0.43 … 4.3307… –0.8440 5)log 4 56 … log(56)/log(4) … 2.9037 6)log 0.3 76 … log(76)/log(0.3) … –3.5970

7. Warmup: Write the form given. Identify it as “Log Form” or “Exponential Form” and then convert it to the other form. 1) 5 x = 56 2) log x+1 (34) = 13 3) log 7 (3x – 2) = 128 4) w (x – 3) = 6y Use your calculator to evaluate the following log values to 4 decimal places. 5) log 546) log 0.64 7)log 4 878) log 6 1.45 9) ln 7810) ln 1.26