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 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 Michelle Vealey

Mathematics

9th - 11th Grade

CCSS covered

Used 211+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When a logarithm has division inside of it, it expands using ________________.

Addition

Subtraction

Multiplication

Division

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

log (-1) =

0.1

.01

all real numbers

does not exist

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write log_b(xy) as two logs

log_bx+log_by

log_bx-log_by

log_bx*log_by

log_bx/log_by

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write log_b(x/y) as two logs

log_bx-log_by

log_bx+log_by

log_bx*log_by

log_bx/log_by

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite log_b(xⁿ)

nlog_bx

(log_bx)ⁿ

xⁿlog_bx

log_b(xⁿ)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

log₅69

log₅56

log₅162

log₅98

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

log 98

log 78

log 56

log 45

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

30 sec • 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

30 sec • 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

10.

MULTIPLE CHOICE QUESTION

30 sec • 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

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Log Properties

When a logarithm has division inside of it, it expands using ________________.

log (-1) =

Write logb(xy) as two logs

Write logb(x/y) as two logs

Rewrite logb(xn)

Write the expression as a single logarithm. Then simplify if possible.log53 + log56 + log59

Write the expression as a single logarithm. Then simplify if possible.log 6 - log 3 + 2 log 7

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)

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Popular Resources on Wayground

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Write log_b(xy) as two logs

Write log_b(x/y) as two logs

Rewrite log_b(xⁿ)

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

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

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

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