Properties of Logarithms

Expand: log₅xy³

• log₅x +log₅y³

• log₅x - log₅y³

• log₅x +3log₅y

• log₅x ⋅ 3log₅y

Condense: log₂x-log₂y-log₂z

• log₂(xz/y)

• log₂(x/yz)

• log₂(xyz)

• log₂(xy/z)

Expand: log₃(5x²y³⁾

• log₃5x² +log₃y³

• log₃5+log₃x² +log₃y³

• log₃5log₃x²log₃y³

• log₃5+2log₃x +3log₃y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand: log₂√x

• log₂x^1/2

• 1/2log₂x

• 2log₂x

• log₂x²

Condense: 1/2(logx - logy)

• log√x / log√y

• log√x / y

• log√xy

• log(√x/√y)

Condense: 1/3 log₄x - log₄y

• log₄(∛x / y)

• log₄∛x / log₄y

• log₄(x³/y)

• log₄x³y

Condense: 5 logx + 4logy + 3logz

• 60log(xyz)

• log(xyz)

• log(x⁵y⁴z³)

• log(x⁵)log(y⁴)log(z³)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand: log₃(x⁵/3y⁴)

• 5log₃x - log₃3 - 4log₃y

• 5log₃x - log₃3 + 4log₃y

• 5log₃x - 4log₃3y

• 5log₃x - 4log₃3 - 4log₃y

Condense: (logx +logy)/2

• log √(xy)

• log(xy/2)

• log(xy²)

• log(x²y²)

Expand: log(4/5)

• log4 +log5

• log4 - log5

• log5 - log4

• log4⁵