Lesson: Precalculus: Solve Logarithmic Equations - 2/14/24

Exponential and logarithmic equations

week of 4/19

A2.F.IF.B.4

Objective

• SWBAT create one variable linear, quadratic, rational, or exponential equations and inequalities IOT use them to solve real-world situations

• SWBAT write or rewrite an exponential function to reveal the percent rate of change and the y-intercept IOT identify key features of the graph and interpret them in a context.

Multiple Choice

Solve for x:
log₄ x = 3

• 4
• 12
• 32
• 64

Multiple Choice

log₃(4x) = 2

• x=4/9

• x=9/4
• x=3/2
• x=2/3

Multiple Choice

Solve for x:

log_x1000=3

• 1

• 10

• 30

• 3

Multiple Choice

log₃(4x) = 2

• x=4/9

• x=9/4
• x=3/2
• x=2/3

Multiple Choice

Solve for x:

log₂(x+3)=4

• 16

• 13

• 3

• 10

Multiple Choice

Solve for x:

log(x+6) = 1

• 4

• 4.222

• -5

• -9.550

Multiple Choice

Solve for x:

log₈(4x+4)=2

• 15

• 12

• 10

• 3

Multiple Choice

Solve: $$\log_7\left(x-3\right)=2$$  

• x = 5

• x = 46

• x = 52

• x = 10

Multiple Select

according to the objective and Title slide: Which functions will we be solving equations for?

• Quadratic

• Exponential

• Linear

• Logarithmic

Multiple Choice

$$Solve\ for\ x.\ 7^{\left(3x+4\right)}=49^{\left(2x+1\right)}$$  

• x = 2

• x = 9

• x = 7/9

• x = 12

Multiple Choice

$$Solve\ for\ x.\ 4^{\left(2x-5\right)}=64^{3x}$$  

• x = -7/5

• x = -5/7

• x = 5

• x = -7

Multiple Choice

2⋅4^{3x – 6} – 8 = 120 (Careful!)

• x = 3

• x = 4

• x = 2.9

• x = 8

Multiple Choice

Solve the equation:

  $$4^{2x\ }=\ 7$$  

• 0

• 1.311

• .364

• .702

Multiple Choice

Solve the equation: 

$$5^{\left(2-3x\right)}=25$$  

• $$\frac{7}{5}$$  

• $$-\frac{3}{4}$$  

• $$-\frac{7}{6}$$  

• $$0$$  

Two forms

1. exponential

2. logaerithmic

Multiple Choice

Solve:

3log₃(x - 5) - 12 = -6

• 25

• 5

• 130

• 14

Multiple Choice

Solve:

2log₆(2x + 3) - 12 = -6

• x = 106.5

• x = 100

• x = 16

• x = 50

Multiple Choice

log(4x+4)=2

• 24

• 12

• -1/2

• -2

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Solve for x.
$$-6\log_{12}\left(x-5\right)=-6$$  

• -1

• -864

• 2

• 17

Multiple Choice

Solve for x.
$$-7\log_2\left(x+9\right)=0$$  

• 6

• -1

• 1.01

• -8

Multiple Choice

Solve:

log₂(2) + log₂(8x) = 6

• x = 3

• x = 2

• x = 6

• x = 4

Multiple Choice

Solve log₅ (x + 3) = log₅ x + log₅ 3

• 3/2

• 9/2

• 2/3

• No Solution

Multiple Choice

Solve:

log₂ x + log₂ (x + 5) = log₂ (3x + 8)

• x = 2

• x = -4

• x = 2 and x = -4

• no solution