Expand: log ⁡ b m n \log_bmn lo g b m n

log ⁡ b m + log ⁡ b n \log_bm+\log_bn lo g b m + lo g b n

log ⁡ b m − log ⁡ b n \log_bm\ -\ \log_bn lo g b m − lo g b n

m log ⁡ b n m\log_bn m lo g b n

n log ⁡ b m n\log_bm n lo g b m

Expand: log ⁡ 6 3 x \log_63x lo g 6 3 x

log ⁡ 6 3 + log ⁡ 6 x \log_63\ +\ \log_6x lo g 6 3 + lo g 6 x

log ⁡ 6 3 − log ⁡ 6 x \log_63-\log_6x lo g 6 3 − lo g 6 x

3 log ⁡ 6 x 3\log_6x 3 lo g 6 x

x log ⁡ 6 3 x\log_63 x lo g 6 3

Expand: log ⁡ a b \log\ ab lo g a b

log ⁡ a + log ⁡ b \log a+\log b lo g a + lo g b

log ⁡ a − log ⁡ b \log a\ -\ \log b lo g a − lo g b

Expand: log ⁡ b m n \log_b\ \frac{m}{n} lo g b n m

log ⁡ b m − log ⁡ b n \log_bm\ -\log_bn lo g b m − lo g b n

log ⁡ b m + log ⁡ b n \log_bm\ +\ \log_b\ n lo g b m + lo g b n

m log ⁡ b n m\log_bn m lo g b n

n log ⁡ b n n\log_bn n lo g b n

Expand: log ⁡ 2 5 x \log_2\ \frac{5}{x} lo g 2 x 5

log ⁡ 2 5 − log ⁡ 2 x \log_25-\log_2x lo g 2 5 − lo g 2 x

log ⁡ 2 5 + log ⁡ 2 x \log_25\ +\ \log_2x lo g 2 5 + lo g 2 x

log ⁡ 2 x − log ⁡ 2 5 \log_2x-\log_25 lo g 2 x − lo g 2 5

5 log ⁡ 2 x 5\log_2x 5 lo g 2 x

Expand: log ⁡ k d \log\ \frac{k}{d} lo g d k

log ⁡ k − log ⁡ d \log\ k\ -\ \log d lo g k − lo g d

log ⁡ k + log ⁡ d \log k\ +\ \log\ d lo g k + lo g d

log ⁡ d − log ⁡ k \log d-\log k lo g d − lo g k

Expand: log ⁡ b m p \log_b\ m^p lo g b m p

p log ⁡ b m p\log_bm p lo g b m

log ⁡ b m + log ⁡ b p \log_bm\ +\ \log_bp lo g b m + lo g b p

log ⁡ b m − log ⁡ b p \log_bm-\log_bp lo g b m − lo g b p

log ⁡ b p − log ⁡ b m \log_bp-\log_bm lo g b p − lo g b m

Expand: log ⁡ d k \log\ d^{\ k} lo g d k

log ⁡ k + log ⁡ d \log k+\log d lo g k + lo g d

log ⁡ d − log ⁡ k \log d\ -\ \log\ k lo g d − lo g k

log ⁡ k − log ⁡ d \log k-\log d lo g k − lo g d

Expand: log ⁡ 9 23 \log_9\sqrt{23} lo g 9 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 2 log ⁡ 9 23 \frac{1}{2}\log_923 2 1 lo g 9 2 3

log ⁡ 9 ( 1 2 ) − log ⁡ 9 23 \log_9\left(\frac{1}{2}\right)-\log_923 lo g 9 ( 2 1 ) − lo g 9 2 3

log ⁡ 9 2 + log ⁡ 9 3 \log_9\sqrt{2}+\log_9\sqrt{3} lo g 9 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + lo g 9 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

log ⁡ 9 ( 1 2 ) + log ⁡ 9 23 \log_9\ \left(\frac{1}{2}\right)+\log_923 lo g 9 ( 2 1 ) + lo g 9 2 3

Expand: log ⁡ 7 4 d \log_74\sqrt{d} lo g 7 4 d <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

log ⁡ 7 4 + 1 2 log ⁡ 7 d \log_7\ 4+\frac{1}{2}\log_7\ d lo g 7 4 + 2 1 lo g 7 d

log ⁡ 7 4 − 1 2 log ⁡ 7 d \log_7\ 4\ -\ \frac{1}{2}\log_7\ d lo g 7 4 − 2 1 lo g 7 d

4 log ⁡ 7 d + log ⁡ 7 1 2 4\log_7d\ +\log_7\ \frac{1}{2} 4 lo g 7 d + lo g 7 2 1

1 2 log ⁡ 4 d \frac{1}{2}\log4d 2 1 lo g 4 d

2 Properties of Logarithms - Expanding

Authored by Cindy Biedrycki

Mathematics

10th - 11th Grade

CCSS covered

Used 799+ times

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18 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_bmn$

$\log_bm\ -\ \log_bn$

$\log_bm+\log_bn$

$m\log_bn$

$n\log_bm$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_63x$

$\log_63\ +\ \log_6x$

$\log_63-\log_6x$

$3\log_6x$

$x\log_63$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log\ ab$

$\log a\ -\ \log b$

$b\log a$

$a\log b$

$\log a+\log b$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_b\ \frac{m}{n}$

$\log_bm\ -\log_bn$

$\log_bm\ +\ \log_b\ n$

$m\log_bn$

$n\log_bn$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_2\ \frac{5}{x}$

$\log_25\ +\ \log_2x$

$\log_2x-\log_25$

$\log_25-\log_2x$

$5\log_2x$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log\ \frac{k}{d}$

$k\log d$

$\log k\ +\ \log\ d$

$\log\ k\ -\ \log d$

$\log d-\log k$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_b\ m^p$

$\log_bm\ +\ \log_bp$

$\log_bm-\log_bp$

$\log_bp-\log_bm$

$p\log_bm$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_7\ y^8$

$\log_7y\ +\ \log_78$

$\log_7y-\log_78$

$8\log_7y$

$\log_78+\log_7y$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log\ d^{\ k}$

$\log k+\log d$

$\log d\ -\ \log\ k$

$\log k-\log d$

$k\log d$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Expand: $\log_9\sqrt{23}$

$\frac{1}{2}\log_923$

$\log_9\left(\frac{1}{2}\right)-\log_923$

$\log_9\sqrt{2}+\log_9\sqrt{3}$

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

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2 Properties of Logarithms - Expanding

Expand: log⁡bmn\log_bmnlogb​mn

Expand: log⁡63x\log_63xlog6​3x

Expand: log⁡ ab\log\ ablog ab

Expand: log⁡b mn\log_b\ \frac{m}{n}logb​ nm​

Expand: log⁡2 5x\log_2\ \frac{5}{x}log2​ x5​

Expand: log⁡ kd\log\ \frac{k}{d}log dk​

Expand: log⁡b mp\log_b\ m^plogb​ mp

Expand: log⁡7 y8\log_7\ y^8log7​ y8

Expand: log⁡ d k\log\ d^{\ k}log d k

Expand: log⁡923\log_9\sqrt{23}log9​23​

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Expand: $\log_bmn$

Expand: $\log_63x$

Expand: $\log\ ab$

Expand: $\log_b\ \frac{m}{n}$

Expand: $\log_2\ \frac{5}{x}$

Expand: $\log\ \frac{k}{d}$

Expand: $\log_b\ m^p$

Expand: $\log_7\ y^8$

Expand: $\log\ d^{\ k}$

Expand: $\log_9\sqrt{23}$