Use the property Log b (xy) = Log b (x) + Log b(y) to expand: Log 3 (5x)

log ⁡ 2 ( 5 ) + log ⁡ 2 ( x ) \log_2\left(5\right)\ +\ \log_2\left(x\right) lo g 2 ( 5 ) + lo g 2 ( x )

log ⁡ 2 ( 5 ) × log ⁡ 2 ( x ) \log_2\left(5\right)\ \times\ \log_2\left(x\right) lo g 2 ( 5 ) × lo g 2 ( x )

log ⁡ 2 ( 5 ) − log ⁡ 2 ( x ) \log_2\left(5\right)\ -\ \log_2\left(x\right) lo g 2 ( 5 ) − lo g 2 ( x )

log ⁡ 2 ( 5 + x ) \log_2\left(5\ +\ x\right)\ lo g 2 ( 5 + x )

Use the property log ⁡ b ( x y ) = log ⁡ b ( x ) − log ⁡ b ( y ) \log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right) lo g b ( y x ) = lo g b ( x ) − lo g b ( y ) to expand log ⁡ 2 ( x 4 ) \log_2\left(\frac{x}{4}\right)\ lo g 2 ( 4 x )

log ⁡ 2 ( x ) − log ⁡ 2 ( 4 ) \log_2\left(x\right)\ -\ \log_2\left(4\right) lo g 2 ( x ) − lo g 2 ( 4 )

log ⁡ 2 ( x ) × log ⁡ 2 ( 4 ) \log_2\left(x\right)\ \times\ \log_2\left(4\right) lo g 2 ( x ) × lo g 2 ( 4 )

log ⁡ 2 ( x ) + log ⁡ 2 ( 4 ) \log_2\left(x\right)\ +\ \log_2\left(4\right) lo g 2 ( x ) + lo g 2 ( 4 )

log ⁡ 2 ( 5 ) − log ⁡ 2 ( x ) \log_2\left(5\right)\ -\ \log_2\left(x\right)\ lo g 2 ( 5 ) − lo g 2 ( x )

Use the change of base property log ⁡ b ( x ) = log ⁡ a ( x ) log ⁡ a ( b ) \log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\ lo g b ( x ) = lo g a ( b ) lo g a ( x ) to write log ⁡ 2 ( 16 ) \log_2\left(16\right)\ lo g 2 ( 1 6 ) with the common base

log ⁡ ( 16 ) log ⁡ ( 2 ) \frac{\log\left(16\right)}{\log\left(2\right)} lo g ( 2 ) lo g ( 1 6 )

log ⁡ ( 8 ) \log\left(8\right) lo g ( 8 )

log ⁡ ( 2 ) log ⁡ ( 16 ) \frac{\log\left(2\right)}{\log\left(16\right)} lo g ( 1 6 ) lo g ( 2 )

log ⁡ ( 16 ) + log ⁡ ( 2 ) \log\left(16\right)\ +\ \log\left(2\right)\ lo g ( 1 6 ) + lo g ( 2 )

Expand log ⁡ 4 ( 6 y ) \log_4\left(6y\right) lo g 4 ( 6 y )

log ⁡ 4 ( 6 ) + log ⁡ 4 ( y ) \log_4\left(6\right)\ +\ \log_4\left(y\right) lo g 4 ( 6 ) + lo g 4 ( y )

log ⁡ 4 ( 6 ) − log ⁡ 4 ( y ) \log_4\left(6\right)\ -\ \log_4\left(y\right) lo g 4 ( 6 ) − lo g 4 ( y )

y log ⁡ 4 ( 6 ) y\log_4\left(6\right)\ y lo g 4 ( 6 )

log ⁡ 4 ( 6 y ) \log_4\left(\frac{6}{y}\right)\ lo g 4 ( y 6 )

Expand log ⁡ 4 ( 3 x y ) \log_4\left(3xy\right) lo g 4 ( 3 x y )

3 log ⁡ 4 ( x ) + 3 log ⁡ 4 ( y ) 3\log_4\left(x\right)\ +\ 3\log_4\left(y\right) 3 lo g 4 ( x ) + 3 lo g 4 ( y )

Expand log ⁡ 2 ( x 3 y ) \log_2\left(\frac{x}{3y}\right) lo g 2 ( 3 y x )

3 log ⁡ 2 ( x ) + log ⁡ 2 ( y ) 3\log_2\left(x\right)\ +\ \log_2\left(y\right) 3 lo g 2 ( x ) + lo g 2 ( y )

log ⁡ 2 ( x ) − 3 log ⁡ 2 ( y ) \log_2\left(x\right)\ -\ 3\log_2\left(y\right) lo g 2 ( x ) − 3 lo g 2 ( y )

Use change of base property to write log ⁡ 16 log ⁡ 3 \frac{\log16}{\log3} lo g 3 lo g 1 6 as one Log

log ⁡ 3 ( 16 ) \log_3\left(16\right)\ lo g 3 ( 1 6 )

log ⁡ 16 ( 3 ) \log_{16}\left(3\right) lo g 1 6 ( 3 )

log ⁡ ( 13 ) \log\left(13\right) lo g ( 1 3 )

log ⁡ ( 19 ) \log\left(19\right) lo g ( 1 9 )

Use properties of Logs to write log ⁡ 3 ( 6 ) + log ⁡ 3 ( 2 ) \log_3\left(6\right)+\log_3\left(2\right) lo g 3 ( 6 ) + lo g 3 ( 2 ) as one Log

log ⁡ 3 ( 12 ) \log_3\left(12\right) lo g 3 ( 1 2 )

log ⁡ 3 ( 8 ) \log_3\left(8\right)\ lo g 3 ( 8 )

log ⁡ 3 ( 4 ) \log_3\left(4\right) lo g 3 ( 4 )

log ⁡ 3 ( 3 ) \log_3\left(3\right) lo g 3 ( 3 )

Use properties of Logs to write log ⁡ 3 ( 8 ) + log ⁡ 3 ( 3 ) − log ⁡ 3 ( 2 ) \log_3\left(8\right)+\log_3\left(3\right)-\log_3\left(2\right) lo g 3 ( 8 ) + lo g 3 ( 3 ) − lo g 3 ( 2 ) as one Log

log ⁡ 3 ( 12 ) \log_3\left(12\right)\ lo g 3 ( 1 2 )

log ⁡ 3 ( 9 ) \log_3\left(9\right) lo g 3 ( 9 )

log ⁡ 3 ( 48 ) \log_3\left(48\right) lo g 3 ( 4 8 )

log ⁡ 3 ( 8 ) \log_3\left(8\right) lo g 3 ( 8 )

Use properties of Logs to write log ⁡ 3 ( 4 ) + log ⁡ 3 ( 3 ) + log ⁡ 3 ( 2 ) \log_3\left(4\right)+\log_3\left(3\right)+\log_3\left(2\right) lo g 3 ( 4 ) + lo g 3 ( 3 ) + lo g 3 ( 2 ) as one Log

log ⁡ 3 ( 24 ) \log_3\left(24\right) lo g 3 ( 2 4 )

log ⁡ 3 ( 9 ) \log_3\left(9\right)\ lo g 3 ( 9 )

log ⁡ 3 ( 6 ) \log_3\left(6\right) lo g 3 ( 6 )

log ⁡ 3 ( 14 ) \log_3\left(14\right) lo g 3 ( 1 4 )

Use properties of Logs to write log ⁡ 3 ( 4 ) − log ⁡ 3 ( x ) + log ⁡ 3 ( y ) \log_3\left(4\right)-\log_3\left(x\right)+\log_3\left(y\right) lo g 3 ( 4 ) − lo g 3 ( x ) + lo g 3 ( y ) as one Log

log ⁡ 3 ( 4 y x ) \log_3\left(\frac{4y}{x}\right) lo g 3 ( x 4 y )

log ⁡ 3 ( 4 x y ) \log_3\left(\frac{4x}{y}\right)\ lo g 3 ( y 4 x )

log ⁡ 3 ( 4 x y ) \log_3\left(4xy\right) lo g 3 ( 4 x y )

log ⁡ 3 ( 4 x y ) \log_3\left(\frac{4}{xy}\right) lo g 3 ( x y 4 )

Use properties of Logs to write 2 log ⁡ 3 ( 4 ) 2\log_3\left(4\right) 2 lo g 3 ( 4 ) as one Log

log ⁡ 3 ( 16 ) \log_3\left(16\right) lo g 3 ( 1 6 )

log ⁡ 3 ( 12 ) \log_3\left(12\right)\ lo g 3 ( 1 2 )

log ⁡ 3 ( 8 ) \log_3\left(8\right) lo g 3 ( 8 )

log ⁡ 3 ( 6 ) \log_3\left(6\right) lo g 3 ( 6 )

Log Properties

Authored by Nicole Baker

Mathematics

10th - 12th Grade

CCSS covered

Used 468+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

16 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use the property Log_b(xy) = Log_b(x) + Log_b(y)
to expand: Log₃(5x)

$\log_2\left(5\right)\ \times\ \log_2\left(x\right)$

$\log_2\left(5\right)\ +\ \log_2\left(x\right)$

$\log_2\left(5\right)\ -\ \log_2\left(x\right)$

$\log_2\left(5\ +\ x\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use the property $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$
to expand $\log_2\left(\frac{x}{4}\right)\$

$\log_2\left(x\right)\ \times\ \log_2\left(4\right)$

$\log_2\left(x\right)\ +\ \log_2\left(4\right)$

$\log_2\left(x\right)\ -\ \log_2\left(4\right)$

$\log_2\left(5\right)\ -\ \log_2\left(x\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use the property $\log_b\left(x\right)^a\ =\ a\log_b\left(x\right)\$
to expand $\log_5\left(x\right)^2\$

$5\log_2\left(x\right)\$

$2\log_5\left(x\right)\$

$\log_5\left(x\right)\ +\ \log_5\left(2\right)$

$\log_5\left(x\right)\ -\ \log_5\left(2\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use the change of base property $\log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\$
to write $\log_2\left(16\right)\$ with the common base

$\log\left(8\right)$

$\frac{\log\left(16\right)}{\log\left(2\right)}$

$\frac{\log\left(2\right)}{\log\left(16\right)}$

$\log\left(16\right)\ +\ \log\left(2\right)\$

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand $\log_4\left(6y\right)$

$\log_4\left(6\right)\ +\ \log_4\left(y\right)$

$\log_4\left(6\right)\ -\ \log_4\left(y\right)$

$y\log_4\left(6\right)\$

$\log_4\left(\frac{6}{y}\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand $\log_4\left(3xy\right)$

$\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$

$3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$

$\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\$

$4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand $\log_2\left(3y^2\right)$

$\log_2\left(3\right)\ +\ \log_2\left(y\right)$

$2\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

$\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

$\log_2\left(\frac{3}{y^2}\right)\$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand $\log_2\left(\frac{x}{3y}\right)$

$\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$

$3\log_2\left(x\right)\ +\ \log_2\left(y\right)$

$\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$

$\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use change of base property to write $\frac{\log16}{\log3}$ as one Log

$\log_3\left(16\right)\$

$\log_{16}\left(3\right)$

$\log\left(13\right)$

$\log\left(19\right)$

Tags

CCSS.HSF.BF.B.5

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use properties of Logs to write $\log_3\left(6\right)+\log_3\left(2\right)$

as one Log

$\log_3\left(8\right)\$

$\log_3\left(4\right)$

$\log_3\left(12\right)$

$\log_3\left(3\right)$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

20 questions

Réduction d'expressions littérales

Quiz

•

7th Grade - University

11 questions

Planteo de Ecuaciones

Quiz

•

1st - 10th Grade

13 questions

Diagrama de cajas y desviación típica

Quiz

•

10th Grade

20 questions

Math 10C Labelling Right Triangles

Quiz

•

8th - 11th Grade

14 questions

Bất phương trình bậc hai

Quiz

•

10th Grade

15 questions

Conocimientos Previos

Quiz

•

5th - 10th Grade

18 questions

Funciones Trigonometricas

Quiz

•

12th Grade

15 questions

Supplementary angles

Quiz

•

7th - 11th Grade

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

22 questions

School Wide Vocab Group 1 Master

Quiz

•

6th - 8th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

12 questions

What makes Nebraska's government unique?

Quiz

•

4th - 5th Grade

Discover more resources for Mathematics

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

10 questions

Factor Quadratic Expressions with Various Coefficients

Quiz

•

9th - 12th Grade

19 questions

Explore Probability Concepts

Quiz

•

7th - 12th Grade

43 questions

STAAR WEEK 1

Quiz

•

9th - 12th Grade

10 questions

Exploring Abiotic and Biotic Factors in Ecosystems

Interactive video

•

6th - 10th Grade

10 questions

Exploring Tree Diagrams in Probability

Interactive video

•

6th - 10th Grade

20 questions

Simple Probability

Quiz

•

10th Grade

11 questions

Solving Quadratic Equations by Factoring

Quiz

•

9th - 12th Grade

Log Properties

Use the property Logb(xy) = Logb(x) + Logb(y)to expand: Log3(5x)

Use the property log⁡b(xy) = log⁡b(x) − log⁡b(y)\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)logb​(yx​) = logb​(x) − logb​(y) to expand log⁡2(x4) \log_2\left(\frac{x}{4}\right)\ log2​(4x​)

Use the property log⁡b(x)a = alog⁡b(x) \log_b\left(x\right)^a\ =\ a\log_b\left(x\right)\ logb​(x)a = alogb​(x) to expand log⁡5(x)2 \log_5\left(x\right)^2\ log5​(x)2

Use the change of base property log⁡b(x) = log⁡a(x)log⁡a(b) \log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\ logb​(x) = loga​(b)loga​(x)​ to write log⁡2(16) \log_2\left(16\right)\ log2​(16) with the common base

Expand log⁡4(6y)\log_4\left(6y\right)log4​(6y)

Expand log⁡4(3xy)\log_4\left(3xy\right)log4​(3xy)

Expand log⁡2(3y2)\log_2\left(3y^2\right)log2​(3y2)

Expand log⁡2(x3y)\log_2\left(\frac{x}{3y}\right)log2​(3yx​)

Use change of base property to write log⁡16log⁡3\frac{\log16}{\log3}log3log16​ as one Log

Use properties of Logs to write log⁡3(6)+log⁡3(2)\log_3\left(6\right)+\log_3\left(2\right)log3​(6)+log3​(2) as one Log

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Use the property Log_b(xy) = Log_b(x) + Log_b(y)
to expand: Log₃(5x)

Use the property $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$
to expand $\log_2\left(\frac{x}{4}\right)\$

Use the property $\log_b\left(x\right)^a\ =\ a\log_b\left(x\right)\$
to expand $\log_5\left(x\right)^2\$

Use the change of base property $\log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\$
to write $\log_2\left(16\right)\$ with the common base

Expand $\log_4\left(6y\right)$

Expand $\log_4\left(3xy\right)$

Expand $\log_2\left(3y^2\right)$

Expand $\log_2\left(\frac{x}{3y}\right)$

Use change of base property to write $\frac{\log16}{\log3}$ as one Log

Use properties of Logs to write $\log_3\left(6\right)+\log_3\left(2\right)$

as one Log