Goes along with 4.4 (GREEN book) _____________________________________________ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ____________________________________________ Intro to Logarithms Goes along with 4.4 (GREEN book)

Definition Logarithms are the "opposite" of exponentials, Logs "undo" exponentials. Logs are the inverses of exponentials.

Writing Logarithms You read it: “Log base b of a equals c” _____________________________________________ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ____________________________________________ You read it: “Log base b of a equals c” ‘log’ is the operation b is the base a is the object of the log c is what you get when you evaluate the log

Exponential Logarithmic Equation Form 103 = 1000 Exponent BASE (The base of the logarithm must be a positive number other than 1.) (You can’t take the log of a negative number or zero. Think about the graph!!)

Exponential Form x y = b Logarithmic Form log x y = b

Example 1: Write 53 = 125 in logarithmic form. Write log381 = 4 in exponential form.

Try This: Complete the table. #1 #2 #3 #4 Exponential Form 25 = 32 3-2 = 1/9 Logarithmic Form log101000 = 3 Log164 = 1/2

Lets look at their graphs (Patty Paper) y = 10x y = log10x y=x

To Evaluate Logs without a Calculator Change the log to an exponential. 1. log2 32 2. log4 2

Solve for x. Change the log to an exponential. 1. log2 64 = x

Evaluate without a calculator: Change the log to an exponential. 1. log 2 8 2. log 2 1 3. Find the value of k : k = log 9 3 4. Find the value of k : ½ = log k 9 5. Find the value of k : 3 = log 7 k

Common Logarithms 10 Logarithms with base ______ are called common logarithms. Sometimes the base is assumed and not written. Thus, if you see a log written without a base, you assume the base is _______. The log button the calculator uses base _____. 10 10

Use your calculator to evaluate: log 51 log 4 log 0.215 1.71 Which means 0.6 – 0.67

Now try these. With a partner, do #5-8 on p. 145 3 – 2 – 6 1/5 x = 2

Do You Know What X is? Change the exponential to a log. Then use calculator. 1. Solve for x: 10x = 728 2. Solve for x: x = 2.86 x = –3.04

Remember e ? The Natural Base Used for applications with CONTINUOUS growth or decay!

Natural Logarithm Think This! Write This! A natural logarithm is a logarithm with base e, denoted by ln. A natural logarithm is the inverse of an exponential function with base e. Think This! Write This! Exponential Form Logarithmic Form

Lets look at their graphs y = ex y = ln x y=x

y = ln x Evaluate f(x)=ln x to the nearest thousandth for each value of x below: ? (see graph) 0.693 – 0.693

With a partner, do #9-12 on p. 146 9. 4.5 –2x 7x 3x

y = ex - 1 y = log5x 13. Find the inverse of y = ln(x+1) 14. Find the inverse of y = 5x . y = ex - 1 y = log5x

Homework P. 147 #7 – 26