Unit 11 Part 2 Logarithms Day 2 Evaluating

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 e 3. 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! 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

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) log 4 56 … log(56)/log(4) … 2. 9037 6) log 0. 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) 5 x = 56 2) logx+1 (34) = 13 3) log 7 (3 x – 2) = 128 4) w(x – 3) = 6 y Use your calculator to evaluate the following log values to 4 decimal places. 5) log 54 6) log 0. 64 7) log 4 87 8) log 6 1. 45 9) ln 78 10) ln 1. 26