Bell work

Find the value to make the sentence true. NO CALCULATOR!! 1. 23 = x 2. 5x = 25 3. (½)3=x4. X (1/2) = 5

• Graph f(x) = 2x

• Name 3 points on f(x)• Graph y = x • Graph f-1 (x)• Write an equation for

the inverse.

F(x) = 2x

to write the equation of the inverse, switch the x and y values

x = 2y How do you solve for y?

Verbally we would say that “Y is the exponent that 2 to raised to in order to get x.”

To write it mathematically: y = log2x

A logarithm is just an exponent

• So the inverse of an exponential function is a logarithmic function. (This means that exponentiation “undoes” logarizing and vice versa.)

Definition of logarithm: X = ay can be rewritten as logax = y

(a>0, a≠1, x>0)** Why is domain positive? ** What # can be raised to power and give you a negative? **

Any exponential expression can be written as a logarithmic expression and vice versa

Rewrite in exponential form. 1. log28 = 3

2. log381=4

3. log164 = ½

4. log273 = ⅓

Any exponential expression can be written as a logarithmic expression and vice versa

Rewrite as a logarithmic expression. 1. 52 = 25 2. 34 = 81 3. (½)3 = ⅛4. (2)-2 = ¼

Remember: A logarithm is an exponent

Evaluate. 1. log216=

** Think: 2 to what power gives me 16?**2. log327= _____

3. log22=_____

4. log101000=____

5. 2 log31= _____

Common logarithm

• The common logarithm is a log with base of 10.

• When the base is 10, we don’t write it!! • Example: log 100 = 2 (Understood base 10) • The calculator uses the common base of 10

when you plug in a value. • Use the calculator to find log 10

Natural logarithm

• The natural logarithm is a log with base e. • Abbreviation is ln• loge5 will be written as ln 5

* “ln” means the base is understood to be e*What is the value of ln e?

Some other important properties that always hold true:

• loga1=0

• logaa=1

• logaax=x

• ln1 = 0

• ln e = 1

• lnex=x

Simplify.

• log55x

• 7log7

14

• log51

If logax=logay, then x=y

• Solve for x:

log2x=log23

• Solve for x:

log44= x

Steps to graphing a logarithmic function

1. Rewrite as an exponential equation

2. Pick values for Y and solve for x

3. Plot the points.

Graph y = log 2x

• Rewrite as Exponential equation: ___________

• Domain: • Range:• Intercepts:• Asymptotes:• How is this related to the

graph y =2x?

Graph f(x) = log3x

• Rewrite as an exponential equation: ___________________

• Domain: • Range: • Intercepts: • Asymptotes:

Graph y = log 4 x

• Rewrite as an exponential equation: ___________________

• Domain• Range• Intercepts• Asymtpotes

Graph y = lnx

• Rewrite as an exponential equation: ___________________

• Domain: • Range: • Intercepts: • Asymptotes:

Graph y = log3(x-2)

• Rewrite as an exponential equation: ___________________

• Domain: • Range: • Intercepts: • Asymptotes:

Transformations

• What happens to the graph of f(x±c)?

Moves right or left c units• What happens to the

graph of f(x) ± c?

Moves the graph up or down c units

• What happens to the graph of f(-x)?

Reflects across the y axis

• What happens to the graph of –f(x)?

Reflects across the x axis

Suppose f(x) = log2xDescribe the change in the graph

1. G(x) = log2(-x)

Reflect over the y axis

2. G(x) = log2 (x+5)

Moves 5 units to the left, VA: x = -5

3. G(x) = -log2(x)

Reflect over the x axis

4. G(x) = log2x-4

Moves the graph down 4 units

5. g(x) = log 2 (x-3)

Moves the graph 3 units to the right, VA: x = 3

Sketch the following graphsDon’t forget RXSRY

1. Y = -lnx

2. Y = ln(-x)

3. Y = ln(x-2)

4. Y = lnx + 3