Solving Log Equations Guided Practice

Solving Log Equations

By Stephanie Balbaneda

Poll

How are you feeling?

• 😊Happy

• 🤪Confused

• 💪Motivated

• 😴Sleepy

In the previous lesson you learned....

• How to convert between log and exponential forms

• The 3 Log properties: Product, Quotient and Power

• How to use the properties to expand/condense log expressions

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)

Condensing/Expanding when more than 1 property is needed:

• Follow the order of operations

• When condensing, always do the Power Property first

Multiple Choice

Condense into one log:   $$2\log_3\left(x\right)+\log_3\left(y\right)$$   Remember to use the power property first!

• $$\log_3\left(2xy\right)\$$

• $$\log_3\left(x^2y\right)$$

• $$\log_3\left(xy\right)^2$$

• $$2\log_3\left(xy\right)$$

Multiple Choice

Condense into a single log expression.

Multiple Choice

Expand:   this has a mix of Product and Quotient Prop.: $$\log\left(\frac{8x}{yz}\right)\$$  

• log8+logx-logy-logz

• log8+logx-logy+logz

• log(8x)-log(yz)

• 8logx-ylogz

Multiple Choice

Expand:    $$\log\left(\frac{m^3}{n}\right)$$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

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?

​Solving Log Equations Guided Practice

Example 1

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

Multiple Choice

Solve $$\log_6x+\log_69=\log_654$$  

• x=6

• x=45

• x=7

• x=36

Example 3

Multiple Choice

Solve

   $$\log_7n=\frac{2}{3}\log_78$$  

• n=1

• n=3

• n=6

• n=4

Example 4

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