1. U6D7
Assignment, red pen, pencil, highlighter, textbook, GP notebook
Have out:
Bellwork:
Evaluate the following. 1) 2) 3) 4) 5) 3 5 –2 –3 +1 +1 +1 +1 +1
total:
Remember: With logarithms, we are looking for exponents.
For example, #1 is read as: “4 to what power is 64?”

2. Logarithms and Logarithmic Functions
Definition of Logarithm
For all positive real numbers x and b , b  1, the inverse of the exponential function y = bx is the logarithmic function ____________.
x = log b y
x = log b y
y = bx
In other words,
____________ if and only if ____________
When converting back and forth between exponential and logarithmic forms, be sure to identify the _____ and _________ first.
base
exponent
exponent
argument
72 = 49
log749 = 2
argument
exponent
base
base

3. I. Write each equation in logarithmic form.b) c) d)
log 9
= 2
log 8
= 3
log
= –2 3 2 8
log
= 2 e) f) g) h)
log
512
= 3
log 10 8
log 16
= –2
log
= –3
100 5

4. 2. Write each equation in exponential form.b) c) 5 3 3
= 243 4
= 64 9
= 3 d) e) f) 2 13
= 169 –2 –1 5 4 g) h)
100 8
= 4

5. I. Inverse Property of Exponents & Logs
Evaluate each expression. a)
= x b)
= x c)
= x d)
= x x 8 x 7
log x
log x 6
= 6 3
= 3 4 5
What patterns do you notice?
In parts (a) and (b), the answer is the “exponent.”
In parts (c) and (d), the answer is the “argument.”
If the bases of the exponential and the logarithmic forms are the _____, then the exponent and logarithm __________ each other.
same
“cancel out”

6. 4. Evaluate each expression.b) c) d) 4
n – 5 45
3x + 2

7. 1. Identify the base & exponent. log2(2x) = 3
II. Solving Logarithmic Equations
Some equations involving logarithms can be solved readily if they are first rewritten in exponential form.
Steps:
Example #1: log2(2x) = 3
exponent
1. Identify the base & exponent.
log2(2x) = 3
2. Write in exponential form by using the definition of logarithms.
base 3
2x = 2
2x = 8
3. Solve for x.
x = 4

8. 1. Identify the base & exponent.
II. Solving Logarithmic Equations
Some equations involving logarithms can be solved readily if they are first rewritten in exponential form.
Steps:
Example #2: log5(4x – 3) = 3
log5(4x – 3) = 3
1. Identify the base & exponent.
exponent
base
2. Write in exponential form by using the definition of logarithms. 3
4x – 3 = 5
4x – 3 = 125
3. Solve for x.
4x = 128
x = 32

9. Finish today's assignment:
Log Worksheet
CC 74 – 76, 78, 79, 81

10. 1) log3x = 5 2) log2x = 3 10) log6(4x + 12) = 2 x = 35 x = 23
Mixed Practice: Solve each equation.
1) log3x = 5
2) log2x = 3
10) log6(4x + 12) = 2
x = 35
x = 23
4x + 12 = 62
4x + 12 = 36
x = 243
x = 8
4x = 24
x = 6