1. Aim: What is the logarithms?
Do Now: Given y = 2x,
1) Graph
2) Write the inverse
function of y = 2x
y = 2x
y = x
x = 2y
HW:
p.323 # 6a,16,18 p.326 # 10,18,36, 38,52,54,58,62, 68

2. x = 2y  y = log2x, same equation different form
The inverse function of y = 2x is x = 2y
we can describe y in the equation x = 2y in words:
y is the exponent to the base 2 needed to obtain x
The word logarithm means exponent,
therefore we can write x = 2y as
y is the logarithm (exponent) to the base 2 of x
In symbolic form, y = log2 x
x = 2y  y = log2x, same equation different form

3. General form of exponential and logarithm function
Exponential function:
f(x) = bx or y = bx
Logarithmic function:
f -1 (x) = logbx or y = logbx
Domain = {x| x > 0}
Range = {y| y Real Number}
Domain = {x| xReal number}
Range = {y| y > 0}

4. Exponential equation Vs. logarithmic equation
Logarithmic equation: log = 3
Exponential equation: 53 = 125
Logarithmic equation: log5 125 = 3
Exponential equation: 43 = 64
Logarithmic equation: log4 64 = 3

5. If
,write f -1(x)
Let f(x) = y, then
Interchange x and y

6. Solve for y in terms of x
1. x = 8y
y = log8x
2. x = 12-y
3. x = log5y
y = 5x

7. 1. Write 82 = 64 in logarithmic form
2. Write log3 81 = 4 in exponential form
34 = 81
3. Write 63 = 216 in logarithmic form
log6 216 =3
4. Write log2 128 = 7 in exponential form
27 = 128

8. Solve for x: logx 8 = 3
Rewrite the logarithmic equation in exponential form
x3 = 8
Use the reciprocal of the exponent to solve for x
Simplify

9. 1. Solve for x: log2 x = 4 16
2. Solve for x: log3 x = –2
1/9 3
3. Solve for b: logb 27 = 3
4. Solve for b: 2