solving logarithmic and exponential equations · 2017-02-07 · 8 notes solving logarithmic and...
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8 Notes Solving Logarithmic and Exponential Equations LB.notebook
1
February 07, 2017
May 54:04 PM
Warmup:1. f(x) = 5x1 4 2. g(x) = 3(2)x+4 + 1
a. Find the inverse of each function.
b. Find the domain and range of the original function and inverse.
c. Find the x and yintercepts of the original and inverse without graphing!
May 39:56 AM
Solving Logarithmic and Exponential Equations
MGSE912.F.BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
MGSE912.F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
MGSE912.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions.
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
2
February 07, 2017
May 54:01 PM
What am I learning today?
How to use logarithmic properties to solve
equations
How will I show that I learned it?Solve equations using exponential and logarithmic
operations and properties
Apr 299:16 AM
Properties of the Natural Logarithm
ln e = 1
ln 1 = 0
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
3
February 07, 2017
May 54:09 PM
Solving Exponential Equations
Type 1: Powers of the same base
• Isolate the exponential part(s).
• Eliminate the base leaving only the exponential part. • Always check your answers!!
May 8 8:53 PM
1) 4 3x = 8 x + 1
2)
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
4
February 07, 2017
Mar 125:30 PM
Type 2: Bases are NOT powers of the same base
• Isolate the exponential part(s).
• Apply a logarithm to each side. Use change of base to help solve.
• Always check your answers!!
May 54:12 PM
3) 2x = 7
Solve for x.
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
5
February 07, 2017
May 54:15 PM
4) 40 e0.6x + 20 = 240
May 54:16 PM
5) 2x = 3x 1 (start on side with more difficult exponent)
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
6
February 07, 2017
May 63:47 PM
Type 3: Logs on each side have same base.
• Every term has loga(?). Condense until each side has only one loga(?).
• Set the answers equal to each other. Then solve.
• Always check your answers!! There are extraneous situations
May 54:23 PM
6) log7(5x 1) = log7(x + 7)
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
7
February 07, 2017
May 39:57 AM
7) ln x ln 9 = ln 3
Apr 295:03 AM
8)
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
8
February 07, 2017
Apr 295:32 AM
9)
May 63:47 PM
Type 4: Log on only one side of the equation!
• Get logx(?) by itself on the one side. Condense if necessary.
• Change the log equation to exponent form. Then solve.
• Always check your answers!! There are extraneous situations.
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
9
February 07, 2017
May 54:24 PM
10) log5(3x + 1) = 2
May 54:28 PM
11) log8(x 3) + log8(x + 4) = 1
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
10
February 07, 2017
Apr 295:36 AM
12)
Dec 54:59 PM
14) 9(123x 5) 75 = 1221Mixed Examples:
15) log4x + log4(x2 3) = log43x
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
11
February 07, 2017
May 63:49 PM
16) ln x + ln (x 5) = 1
4) 13216 2x + 1 =
May 54:28 PM
5) 15 2log4(28x + 8) = 3
6) 5 x 3 = 341
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
12
February 07, 2017
May 57:32 PM
7) log5(9x 1) = log5(4x 16)
8) 3 ln ( x) + 9 = 20
May 57:35 PM
9) 102x 3 + 4 = 21
10) log6(x + 5) + log6x = 2
8 Notes Solving Logarithmic and Exponential Equations LB.notebook
13
February 07, 2017
May 57:35 PM
11) 3 + 5x = 21
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