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 )

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

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

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

10th - 12th Grade

•

16 Qs

Similar activities

EVALUACION VIRTUAL 3 AREA DE MATEMATICA 5° DE SECUNDARIA -JAPAM

12th Grade

•

15 Qs

Statistika SMK

10th - 12th Grade

•

11 Qs

Opfrissertje rekenen 4

1st - 10th Grade

•

20 Qs

Examen Primera Unidad

10th Grade

•

20 Qs

Ulangan Harian Prolin IPS

KG - 11th Grade

•

20 Qs

Mengenal lebih jauh siswa MAN 2 Kota Malang angkatan 31

9th - 10th Grade

•

11 Qs

PTS MATEMATIKA MINAT XII

12th Grade

•

20 Qs

X_Bentuk Akar Kuis 2 =020924

10th Grade

•

15 Qs

Log Properties

Quiz

•

Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSA.SSE.B.3, HSF.BF.B.5, HSF.IF.C.8

Standards-aligned

Nicole Baker

Used 468+ times

FREE Resource

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.A.2

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 $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$
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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Create a free account and access millions of resources

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

15 questions

Conocimientos Previos

Quiz

•

5th - 10th Grade

18 questions

Funciones Trigonometricas

Quiz

•

12th Grade

15 questions

Supplementary angles

Quiz

•

7th - 11th Grade

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

POTENCIACIÓN NIVEL I

Quiz

•

1st Grade - University

14 questions

Bất phương trình bậc hai

Quiz

•

10th Grade

Popular Resources on Wayground

5 questions

This is not a...winter edition (Drawing game)

Quiz

•

1st - 5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

20 questions

Christmas Trivia

Quiz

•

6th - 8th Grade

18 questions

Kids Christmas Trivia

Quiz

•

KG - 5th Grade

11 questions

How well do you know your Christmas Characters?

Lesson

•

3rd Grade

14 questions

Christmas Trivia

Quiz

•

5th Grade

20 questions

How the Grinch Stole Christmas

Quiz

•

5th Grade

Discover more resources for Mathematics

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

33 questions

Algebra 1 Semester 1 Final 2025

Quiz

•

8th - 10th Grade

10 questions

Exploring Global Holiday Traditions

Interactive video

•

6th - 10th Grade

10 questions

Guess the Christmas Movie by the Scene Challenge

Interactive video

•

6th - 10th Grade

10 questions

Guess the Christmas Songs Challenge

Interactive video

•

6th - 10th Grade

10 questions

Test Your Christmas Trivia Skills

Interactive video

•

6th - 10th Grade

10 questions

Exploring the Grinch's Christmas Heist

Interactive video

•

6th - 10th Grade

20 questions

Christmas Lyrics

Quiz

•

12th Grade

Log Properties

16 questions

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\$