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Warm Up
Evaluate the following.
1. f(x) = 2x when x = -0.25
2. f(x) = log x when x = 4.3
3. f(x) = 3.78x when x = 0.10
4. f(x) = ln x when x = 0.152
5. f(x) = -5x when x = .94
6. f(x) = log4 x when x = 1024
Graphing Exponentials and
Logarithms
March 18, 2013
Objective
• SWBAT identify the graphs of exponential and
logarithmic functions
• SWBAT graph exponential and logarithmic
functions through transformations
Vocabulary
Exponential
Growth
An exponential function
that is always increasing
Exponential
Decay
An exponential function
that is always decreasing
Domain of a Log Set the inside of the log ≥
0 and solve for x
Exponential Growth
Basic Exponential Function f(x) = ax, a > 1
• Domain: All Real Numbers
• Range: Positive Numbers
• Intercept: (0, 1)
• Increasing
• Horizontal Asymptote: y= 0
Exponential Decay
Basic Exponential Function f(x) = a-x, a >1
• Domain: All Real Numbers
• Range: Positive Numbers
• Intercept: (0, 1)
• Decreasing
• Horizontal Asymptote: y= 0
Logarithmic
Basic Logarithmic Function f(x) = loga x, a > 1
• Domain: Positive Numbers
• Range: All Real Numbers
• Intercept: (1, 0)
• Increasing
• Vertical Asymptote: x = 0
• Reflection of y = ax across the line y = x
Identifying Type of Function
• Look for intercepts and asymptotes
• Look for increasing or decreasing behavior
Example
1.
2.
Practice
Solving Exponential Equations
Objective
• SWBAT solve exponential and logarithmic
equations
Vocabulary
Exponential Equation
y = bx
Logarithmic Equation
x = logb y
Solving Exponential Equations
1. Simplify the equation so the exponential is
isolated on one side of the equal sign
2. Rewrite the equation as a logarithm using the
definition
3. Decide if an exact answer or an approximate
solution is preferable
Solving Simple Equations
• In general there are two strategies for solving
exponential and logarithmic equations, look
for opportunities to use the one-to-one
property or use the inverse property.
• In either case, first rewrite the equation to see
which property should be used then solve for
x
Example
1. 2x = 32
Example
• (1/3)x = 9
Example
1. 3(2x) = 42
Example
2. ex + 5 = 60
Example
3. 2(32t-5) – 4 = 11
Practice
1.
2.
3.
4.
5.
6.
ex = 7
4x = 64
3x = 1/9
2(5x) = 32
4ex = 91
2x-3 = 32
7. e2x = 50
8. -14 +3ex = 11
9. 8(36-2x) + 13 = 41
10.6 – 3(42x-1) = -27
11.7(93x+8) = 63
12.8(e7x+1) – 9 = 7
Solving Logarithmic Equations
• Simplify the equation so the logarithm is
isolated on one side of the equal sign
• Rewrite the equation as a exponential using
the definition
• Decide if an exact answer or an approximate
solution is preferable
Example
1. ln x = -3
Example
• log10 x = 2
Example
• log4 (3x) = 4
Example
• 3 log5 (x + 1)= -6
Practice
1.
2.
3.
4.
5.
ln x = 7
log4 x = 4
2 log5 x = 2
4 ln x = 16
log2 (x – 3) = 3
6. ln (2x) = 5
7. -14 + 3 ln x = 10
8. 8log3(6-2x)+13=35
9. 6–3log4(2x–1)=-24
10. 8ln(7x + 1) – 9 = 7