Solving Logarithmic Equations

Solving Logarithmic Equations

Review

• Product Rule : $\log_amn=\log_am+\log_an$   

• Quotient Rule:  $\log_a\left(\frac{m}{n}\right)=\log_am-\log_an$  

• Power Rule: $\log_a\left(m\right)^n=n\log_am$  

• Equality Rule: If $\log_am=\log_an$  then, m=n

Solving Log Equations

Things to keep in mind:

-Are the bases of the logs the same?

- Is there any property we can use to simplify the equation?

Example 1

 $\log_3\left(x+4\right)=\log_3\left(9\right)$  

Multiple Choice

Solve  $\log_2\left(x+8\right)=\log_264$  

• x=16

• x=24

• x=56

• x=40

Multiple Choice

Solve $\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$  

•  $x=\frac{3}{4}$  

•  $x=3$  

•  $x=6$   

•  $x=\frac{4}{3}$  

Example 2

 $\log_2x+\log_28=\log_232$  

Multiple Choice

Solve  $\log_6x+\log_69=\log_654$  

• x=6

• x=45

• x=7

• x=36

Example 3

 $\log_2n=\log_216^{\frac{3}{4}}$  

Multiple Choice

Solve

   $\log_7n=\frac{2}{3}\log_78$  

• n=1

• n=3

• n=6

• n=4

Example 4

 $\log_6\left(n+15\right)-\log_63=\log_62n$  

Multiple Choice

Solve $\log_9\left(3u+14\right)-\log_95=\log_92u$  

• u=4

• u=6

• u=2

• u=1

Poll

Which of the following best describes your understanding of this lesson?

• Mastered

• Good understanding

• Need more practice

• I don't understand