10.4 Solving Log Equations

Solving Log/Natural Log Equations

LO: SWBAT solve Log & Natural Log Equations
DOL: SWBAT acquire at least a 70% proficiency in the given exercises involving solving Log & Natural Log Equations

Match

Expand the following expressions

• $$\log x^3y^4$$

• $$\log2x^3$$

• $$\log xy^2$$

• $$\log x^4y^3$$

• $$3\log x+4\log y$$

• $$\log2+3\log x$$

• $$\log x + 2\log y$$

• $$4\log x + 3\log y$$

​Solving Log Equations

1. Condense to a single log

2. Isolate the log

3. Rewrite as an exponent (Fishhook)

4. Solve for x

​Steps To Solve

Reorder

Reorder the following

• Condense to one log

• Isolate the log

• Rewrite as an exponent

• solve for x

1

2

3

4

• 1
• 2
• 3
• 4

Open Ended

Given the equation to the left explain why is step 1 already complete?

Math Response

Isolate the log and rewrite the equation

(Hint: Move the 2 over and then the 4. How could you do that?)

Type answer here

Correct Answer: \log_4\left(x\right)=-1

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Math Response

Rewrite as an exponential equation using the fish hook method

Type answer here

Correct Answer: 4^{-1}=x

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Math Response

Solve for x

(Hint: Can you have negative exponents?)

Put x =

Type answer here

Correct Answer: \frac{1}{4}=x

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​Solving With 2 Logs

​The same 3 steps are used here but each step requires you to apply prior knowledge to complete the step. i.e. to condense you must know all the rules.

​Guided Practice

Math Response

On your whiteboard solve the following logarithmic equation

Put x =

Type answer here

Correct Answer: x=\frac{8}{245}

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Open Ended

What do you notice is different with this example compared to the others we have completed.

​Solving Natural Log Equations

​Follow along in your notes you will be responsible for the next example!!

Math Response

Solve the following natural log equation on your whiteboards and type your answer in.

Use the letter "v" as a replacement for "e" because Quizziz is silly.

Type answer here

Correct Answer: x=\frac{v^{-2}-1}{6}

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