1. Assignment, red pen, highlighter, textbook, GP notebook, pencil
U6D6
Have out:
Bellwork:
Solve for x. Approximate to 2 decimal places when appropriate. 1) 2) 3) 3 3 +1 +2
#1 & #2 were some of the most missed questions on the Unit 4 test. +1 +1 +1 +1
Will this PowerPoint burst into flames???
Is this end of math as we know it????
No solution??? +1 +1
total: +1
Whew, that was a close one!

2. Introduction to Logarithms
Copy onto your
worksheet:
Introduction to Logarithms
Sketch y = f(x) for f(x) = 10x.
We know the graph of the inverse function f–1(x) will be the __________ of y = f(x) across the line of _________. y x 10
-10
y = x x
f(x) –1 1
reflection
reflection
f–1(x)
f(x) = 10x 1 10
Sketch y = f–1(x) and y = x.

3. What is f–1(x)? What undoes the exponential function?y x 10
-10 y
y = x
logarithm
The ___________ function is the inverse (or undoes) the exponential function.
f–1(x)
f(x) = 10x
Notation:
f–1(x) = log10x x
The “10” is called the _____ of the logarithm, just like it is the base in the exponential function.
base
common
“10” is also called the _________ logarithm, so we omit the 10.
log x
log10x
Therefore _________ implies _________.
(This is similar to the unwritten “one” for coefficients or exponents.)

4. When we use the logarithmic function, we are looking for an _________.
exponent
10 to what power is equal to 100?
log 100 means “_____________________________” 2
log 100 = ____
Practice: 3 –1 –2 4 –3

5. For each function, sketch y = f(x), y = f–1(x), and y = x
For each function, sketch y = f(x), y = f–1(x), and y = x. Determine f–1(x).
f(x) = 2x
a) f(x) = 2x
y = x y x 1 2 3 4 5 -1 -2 -3 -4 -5
(–∞, ∞) x
f(x) –2 –1 1 2
Domain: _______
f–1(x)
(0, ∞)
Range: _______ 1 2 4
log2x
f–1(x) = _______
f–1(x) = log2(x)
(0, ∞)
f(x) = 2x
Domain: _______
(–∞, ∞)
Range: _______
same base

6. For each function, sketch y = f(x), y = f–1(x), and y = x
For each function, sketch y = f(x), y = f–1(x), and y = x. Determine f–1(x).
f(x) = 5x
b) f(x) = 5x
y = x y x 1 2 3 4 5 -1 -2 -3 -4 -5
(–∞, ∞) x
f(x) –1 1
Domain: _______
(0, ∞)
Range: _______ 1
f–1(x) 5
log5x
f–1(x) = _______
(0, ∞)
Domain: _______
(–∞, ∞)
Range: _______
f(x) = 5x
f–1(x) = log5(x)
Given b > 0, f(x) = logbx has domain ____ and range ______.
(0, ∞)
(–∞, ∞)
same base

7. Practice: Simplify these logarithmic expressions.
Recall: “the base to what power is…?” 2 4 3 5 –2 –4 –2 –3 –3 –3
Click here

8. Finish today's assignment:
Log Mixed Practice &
CC 60, 61, 64, 66, 68