Exponential and Logarithmic Equations

Intro to Exponential and Logarithmic Equations

Have out note paper so you can write these down and try them out!

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

• ln(wvu⁵)
• ln(u + v + w⁵)
• ln(uvw⁵)
• ln(uvw)⁵

Multiple Choice

Solve for x.
3^x = 27

• 2
• 4
• 3
• 5

Multiple Choice

When a logarithm has multiplication inside of it, it expands using ________________.

• Addition
• Subtraction
• Multiplication
• Division

Multiple Choice

Condense. 

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Select

What two logarithm buttons can be found on the calculator?

• Log with a base of 2

• Log with a base of 3

• Log with a base of 10

• Log with a base of e

Multiple Choice

What does  $\log_bb$  equal?

• 0

• 1

• 2

• b

How do we solve more complex equations using these log properties and skills?

Take a few notes on the ways to solve different types of equations from the next page. Use the examples on the page to practice these skills. There are a few questions from the beginning sections in the next few slides to check for understanding.

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Fill in the Blanks

Solve for x (No spaces!)

  $3^{\left(x-4\right)}=3^{\left(3x+2\right)}$  

Fill in the Blanks

 $32^x=64$  

What is x? 
No spaces!

Using Logarithms to Solve Exponential Equations

Pay special attention to this section and try out that method here! (You will find this subtitle on the webpage for your notes, look there for help.)

Multiple Select

Solve the following equation. Select all possible solutions.

 $4^{\left(x-2\right)}=13$  

• x =  $\frac{\ln\left(13\right)}{\ln\left(4\right)}+2$  

• x =  $\log_413+2$  

• x =  $\log_{13}4+2$  

•  $x\ =\ \frac{\log13}{\log4}+2$  

• x =  $\frac{\log4}{\log13}+2$  

Multiple Select

Solve for x. Select all solutions below.

 $2^x=3^{\left(x+1\right)}$  

•  $-1,\ 1$  

•  $\approx-2.710$  

•  $\frac{\log3}{\log\left(\frac{2}{3}\right)}$  

•  $\log_23-1$  

•  $\frac{\log3}{\log2}-1$  

Multiple Select

Solve for x. Select all solutions below.
 $2^{\left(x-4\right)}=11$  

•  $\approx5.354$  

•  $\frac{\ln\left(11\right)}{\ln\left(2\right)}+4$  
  

•  $\log_211+4$  

•  $\log_{11}2+4$  

• None of the above

Poll

How do you feel about just those skills so far?

• 1 - VERY CONFUSED!

• 2 - Not great, but I pieced together some of it

• 3 - I'm going to need more practice, but it's starting to make sense

• 4 - I need practice, but I'm doing pretty well!

• 5 - This is a walk in the park, can I teach next class?

That's all for now!

We will see more examples like the others on that webpage next class, just getting a handle on those exponential questions will at least get us prepared for next class.

I will see you all then!