Choose the correctly condensed logarithm 1 2 log ⁡ 6 a − log ⁡ 6 b + log ⁡ 6 6 \frac{1}{2}\log_6a-\log_6b+\log_66 2 1 lo g 6 a − lo g 6 b + lo g 6 6

log ⁡ 6 ( a b ) + 1 \log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +1 lo g 6 ( b a <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

log ⁡ 6 ( 6 a b ) \log_6\left(\frac{6\sqrt{a}}{b}\right)\ lo g 6 ( b 6 a <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 ⁡ 6 ( a b + 1 ) \log_6\left(\frac{\sqrt{a}}{b}+1\right)\ \ lo g 6 ( b a <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 )

log ⁡ 6 ( a b ) + 6 \log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +6 lo g 6 ( b a <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"> ) + 6

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

46 Practice: Expanding and Condensing Logarithms

Authored by Christy Nunnally

Mathematics

9th - 12th Grade

CCSS covered

Used 13+ times

46 Practice: Expanding and Condensing Logarithms

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand

6log₈v-2log₈u

6log₈u-2log₈v

3log₈u-2log₈v

6log₈u+2log₈v

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Condense

logxyz³

log(xy/z³)

logx+logy+logz³

logx³y³z³

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Condense

logxyz³

log(xy/z³)

logx+logy+logz³

logx³y³z³

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Expand

6log₈v-2log₈u

6log₈u-2log₈v

3log₈u-2log₈v

6log₈u+2log₈v

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Condense.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$

$\log_6\left(\frac{6\sqrt{a}}{b}\right)\$

$\log_6\left(\frac{\sqrt{a}}{b}+1\right)\ \$

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +1$

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +6$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

log(x) + log(z) + 4log(y)

3log(x) − log(z) − 4log(y)

3log(x) + log(z) + 4log(y)

log(x) − 4log(z) − 3log(y)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

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46 Practice: Expanding and Condensing Logarithms

Expand

Condense

Condense

Expand

Condense.

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$

Condense: ln5 + 3lnx - 2lny

Expand each Log

Expand each Log

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46 Practice: Expanding and Condensing Logarithms

Expand

Condense

Condense

Expand

Condense.

Choose the correctly condensed logarithm 12log⁡6a−log⁡6b+log⁡66\frac{1}{2}\log_6a-\log_6b+\log_6621​log6​a−log6​b+log6​6

Condense: ln5 + 3lnx - 2lny

Expand each Log

Expand each Log

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Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$