Logarithms 4317 Lets check out Desmos What is

Logarithms 4/3/17

Let’s check out Desmos ▪ What is a Log function?

Conversions Think: base stays the same, x and y switch places log 28 = 3 23 = 8

For example log 3 27 = y log 5 125 = 3 log 8 2 = 1/3 log 4 1/256 = -4

How about the other way? 153 = 3375 41/2 = 2 3 -3 = 1/81 53 X = 100

Try these! log 4 16 = 2 log 3 729 = 6 43 = 64 1251/3 = 5

Homework ▪ Homework: Problem set 4 and 5

What about evaluating? ▪

Solving for the base ▪

Real quick. . . What is ANYTHING to the zero power? 30 x 0 -130

Practice ▪

Graphing Logs

Get out your calculators! ▪ Graph log(x) Draw where the values go here

y What does this mean for domain/range? What about asymptotes?

Graph each function ▪

Transformations

Practice ▪

Homework ▪ Homework: Problem set 11 #’s 1 -4

Changing Bases

Find the following ▪

Change of Base Formula

Euler’s constant e https: //www. youtube. com/watch? v =b-MZumdfbt 8 e = 2. 71828………… Natural log = ln NOT in

▪ Pretty much, can be written as or The is what we write as ln (natural log).

Same properties apply, let’s rewrite!

Practice!

Solving equations with e Exact same steps as what we have already done. 1. Get the same bases 2. Use the definition to solve for the exponents 3. Use any properties in the exponents 4. Solve

Graphing the natural log What are your thoughts Do we need to try Desmos again?

Compound Interest Formula ▪

You deposit $1500 in an account that pays 7. 5% interest compounded continuously. What is the balance after 3 years?

Try problems 3, 5, and 6.

▪ Homework: Problem set 10