Expand and FULLY simplify: log ⁡ ( 100 z ) \log\left(100\sqrt{z}\right) lo g ( 1 0 0 z <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"> )

2 + 1 2 log ⁡ ( z ) 2+\frac{1}{2}\log\left(z\right) 2 + 2 1 lo g ( z )

log ⁡ ( 100 ) + log ⁡ ( z ) 2 \log\left(100\right)+\frac{\log\left(z\right)}{2} lo g ( 1 0 0 ) + 2 lo g ( z )

100 + z 100+\sqrt{z} 1 0 0 + z <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 ⁡ ( 100 ) + log ⁡ ( z ) \log\left(100\right)+\log\left(\sqrt{z}\right) lo g ( 1 0 0 ) + lo g ( z <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"> )

After condensing log ⁡ 4 ( 9 ) + log ⁡ 4 ( 8 ) − log ⁡ 4 ( 4.5 ) \log_4\left(9\right)+\log_4\left(8\right)-\log_4\left(4.5\right) lo g 4 ( 9 ) + lo g 4 ( 8 ) − lo g 4 ( 4 . 5 ) , it is equivalent to TWO of the following choices. Which ones?

log ⁡ 4 ( 16 ) \log_4\left(16\right) lo g 4 ( 1 6 )

log ⁡ 4 ( 12.5 ) \log_4\left(12.5\right) lo g 4 ( 1 2 . 5 )

Logarithm Laws Quiz

Authored by Nikki Upham

Mathematics

10th - 12th Grade

CCSS covered

Used 26+ times

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20 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Condense

log(xyz³)

log(xy/z³)

log(x)+log(y)+log(z³)

log(x³y³z³)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Expand

log₈x+log₈y+log₈z

5log₈x+5log₈y+5log₈z

log₈xy+5log₈z

log₈x+log₈y+5log₈z

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Condense

log₈(a¹⁸/b³)

log₈(a¹⁸b³)

log₈(a/b³)

15log₈(a/b³)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Expand

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The common logarithm has what base?

-e

Tags

CCSS.HSF.BF.B.5

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Logarithm Laws

Condense

Expand

Condense

Expand

The common logarithm has what base?

Expand the following logarithm:
log₂ 5x.

Expand the following logarithm:
log₃ 10z

Expand the following logarithm:
log₂ 6/y

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Logarithm Laws

Condense

Expand

Condense

Expand

The common logarithm has what base?

Expand the following logarithm: log2 5x.

Expand the following logarithm: log3 10z

Expand the following logarithm: log2 6/y

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Expand the following logarithm:
log₂ 5x.

Expand the following logarithm:
log₃ 10z

Expand the following logarithm:
log₂ 6/y