 # Bell work Find the value to make the sentence true. NO CALCULATOR!!

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Bell work Find the value to make the sentence true. NO CALCULATOR!!
23 = x 5x = 25 (½)3=x 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. log28 = 3 log381=4 log164 = ½ log273 = ⅓

Any exponential expression can be written as a logarithmic expression and vice versa
Rewrite as a logarithmic expression. 52 = 25 34 = 81 (½)3 = ⅛ (2)-2 = ¼

Remember: A logarithm is an exponent
Evaluate. log216= ** Think: 2 to what power gives me 16?** log327= _____ log22=_____ log101000=____ 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 7log714 log51

If logax=logay, then x=y
Solve for x: log2x=log23 Solve for x: log44= x

Steps to graphing a logarithmic function
Rewrite as an exponential equation Pick values for Y and solve for x 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) = log2x Describe the change in the graph
G(x) = log2(-x) Reflect over the y axis G(x) = log2 (x+5) Moves 5 units to the left, VA: x = -5 G(x) = -log2(x) Reflect over the x axis G(x) = log2x-4 Moves the graph down 4 units g(x) = log 2 (x-3) Moves the graph 3 units to the right, VA: x = 3

Sketch the following graphs Don’t forget RXSRY
Y = -lnx 2. Y = ln(-x) Y = ln(x-2) Y = lnx + 3

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