Solving Log Equations

Solving Log Equations

Yay!

Recall

• Product Rule: log_a(m*n) = log_am+log_an

• Quotient Rule: log_a(m/n) = log_am-log_an

• Exponent Rule: y*log_a(m) = log_a(m^y)

New Rule: The Equality Rule

• If log_a(x) = log_a(y), the x = y

• So log(x) = log(7), this means that x = 7

• Recall we had a very similar rule when solving exponentials, b^x = b^y, x = y, why does it make sense that we have a similar rule?

Multiple Choice

Solve log₂(x+8)=log₂(64)

• 16

• 24

• 56

• 40

Multiple Choice

Solve log(3x+7) = log(7x+4)

• $\frac{3}{4}$

• 7

• 5

• $\frac{4}{3}$

Steps to Solving a Log Equation

log₄(x)+log₄(7)=log₄(35)

• Step 1) Use log rules and arithmetic to make it so there's only one log per side: log₄(7x) = log₄(35)

• Step 2) Use the Equality Rule to set the insides equal to each other: 7x = 35

• Step 3) Solve! x = 5

Multiple Choice

Solve 

 $\log_6\left(9\right)+\log_6\left(x\right)=\log_6\left(54\right)$  

• 7

• 9

• 6

• 5

Multiple Choice

Solve

 $\log_4\left(x\right)-\log_4\left(8\right)=\log_45$  

• 40

• 300

• 4

• 8

Multiple Choice

Solve (Careful this one is a bit tricky)

 $\log_{ }\left(x+7\right)-\log_{ }\left(x\right)=\log_{ }\left(2\right)$  

• 4

• 5

• 7

• 9

Example

 $\log_2\left(x\right)=\frac{3}{4}\log_2\left(16\right)$  

Multiple Choice

Solve

 $\log_3\left(x\right)=\frac{2}{3}\log_3\left(8\right)$  

• 4

• 16

• 32

• 64

Poll

How would you describe your understanding of this material?

• Mastered

• Good Understanding

• Need More Practice

• I don't Understand