Convert Between Exponents and Logarithms

Converting Exponential to Logarithmic Equations

April 7/8

Multiple Choice

3² = 9

• log ₃ 2 = 9

• log ₉ 3 = 2

• log ₃ 9 = 2

• log ₂ 9 = 3

Multiple Choice

5³ = 125

• log ₅ 125 = 3

• log ₃ 5 = 125

• log ₁₂₅ 3 = 5

• log ₅ 3 = 125

Multiple Choice

16 = 4²

• log ₄ 2 = 16

• log ₁₆ 4 = 2

• log ₂ 16 = 4

• log ₄ 16 = 2

Multiple Choice

2⁵ = 32

• log ₅ 32 = 2

• log ₂ 32 = 5

• log ₃₂ 5 = 2

• log ₂ 5 = 32

Multiple Choice

7^x = 13

• log ₇ x = 13

• log ₁₃ x = 7

• log ₇ 13 = x

• log _x 7 = 13

Multiple Choice

b^k = m

• log _b m = k

• log _m k = b

• log _b k = m

• log _k m = b

Multiple Choice

10³ = 1000

• log ₁₀₀₀ 3 = 10

• log ₃ 10 = 1000

• log 3 = 1000

• log 1000 = 3

Multiple Choice

What is the logarithmic form of the exponential function?

$$6^{-3}=\frac{1}{216}$$  

• $$\log_{-3}6=\frac{1}{216}$$  

• $$\log_6\left(\frac{1}{216}\right)=-3$$  

• $$\log_6-3=\frac{1}{216}$$  

• $$\log_6\left(\frac{1}{216}\right)=3$$  

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

What is the exponent form of the following logarithmic function? 

$$\log_84=\frac{2}{3}$$

• $$8^4=\frac{2}{3}$$  

• $$8^{\frac{2}{3}}=4$$  

• $$4^{\frac{2}{3}}=8$$  

• $$4^8=\frac{2}{3}$$  

Multiple Choice

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Multiple Choice

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Multiple Choice

Rewrite log₂8 = 3 in exponential form/

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Multiple Choice

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Multiple Choice

Convert the exponential form $$5^3 = 125$$ into its equivalent logarithmic form.

• $$\log_5{125} = 3$$

• $$\log_5{3} = 125$$

• $$\log_{125}{5} = 3$$

• $$\log_{3}{125} = 5$$

Multiple Choice

Convert the exponential form to logarithmic form: $$2^3 = 8$$

• $$\log_2(8) = 3$$

• $$\log_8(2) = 3$$

• $$\log_3(2) = 8$$

• $$\log_2(3) = 8$$

7.4 - Properties of Logarithms

​

Recall:

More:

Practice next:

Product Property

Example

Multiple Choice

Condense

$$\log_35+\log_34$$  

• $$\log_39$$  

• $$\log_320$$  

• $$\log_69$$  

• $$\log_620$$  

Multiple Choice

Condense

$$\log_53+\log_5y+\log_5z$$  

• $$\log_53yz$$  

• $$\log_{15}3yz$$  

• $$\log_35yz$$  

• $$\log_z15y$$  

Multiple Choice

Expand

$$\log_28y$$  

• $$\log_82+\log_8y$$  

• $$\log_28+\log_2y$$  

• $$\log_2y+\log_82$$  

• $$\log_y2+\log_y8$$  

Quotient Property

Multiple Choice

Condense

$$\log_7y-\log_79$$  

• $$\log_7\frac{9}{y}$$  

• $$\log_79y$$  

• $$\log_7\frac{y}{9}$$  

• $$\log_9\frac{y}{7}$$  

Multiple Choice

Expand

$$\log_4\frac{y}{10}$$  

• $$\log_4y+\log_410$$  

• $$\log_410-\log_4y$$  

• $$\log_{10}y-\log_{10}4$$  

• $$\log_4y-\log_410$$  

Power Property

Multiple Choice

Condense

$$3\log_47$$  

• $$\log_47^3$$  

• $$\log_421$$  

• $$\log_43^7$$  

• $$\log_410$$  

Multiple Choice

Expand

$$\log_2^{ }y^5$$  

• $$y\cdot\log_25$$  

• $$5\log_2y$$  

• $$2\cdot\log_5y$$  

• $$\log_25^y$$  

Multiple Choice

Rewrite $$\log\left(5\right)+\log\left(4\right)$$  as  $$\log\left(c\right)$$  

• $$\log20$$  

• $$\log9$$  

• $$\log1$$  

Multiple Choice

Write log_b(xy) as two logs

• log_bx+log_by

• log_bx-log_by

• logbx*logby

• log_bx/log_by

Multiple Choice

Rewrite as a single logarithm:

$$\log_260\ -\ \log_210$$  

• $$\log_26$$  
  

• $$\log_250$$  
  

• $$\frac{\log_260}{\log_210}$$  
  

• $$\log_270$$