Expanding and Condensing Logarithms

Expand: log₂x⁶

• xlog₂6

• log₂x - log₂6

• log₂x + log₂6

• 6log₂x

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

Expand: log₅8x

• xlog₅8

• log₅8 + log₅x

• log₅8 - log₅x

• 8log₅x

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand: ln(5x⁷)

• ln5 - 7lnx

• ln5 + lnx + ln7

• ln5 + 7lnx

• ln5x - ln7

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

Expand:

• log₆y - log₆2

• log₆y + log₆2

• 2log₆y

• ylog₆2

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

Expand:

• 3log₅7x

• 3log₅x + log₅7

• log₅7 - 3log₅x

• 3log₅x - log₅7

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Expand:

• 2lnx - ln 6

• ln6 - 2lnx

• ln6 + 2lnx

• 2ln6x

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

Expand: log₈6x³y

• log₈6 + log₈x - 3log₈y

• 3log₈6 - log₈x + log₈y

• log₈6 + 3log₈x - log₈y

• log₈6 + 3log₈x + log₈y

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Condense: 5log₈y

• log₈5^y

• $\log_8\left(\frac{y}{5}\right)$

• log₈5y

• log₈y⁵

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

Condense: log6 + logx

• $\log x^6$

• $\log6x$

• $\log\left(\frac{6}{x}\right)$

• $\log6^x$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Condense: log₅7 + 2log₅x

• log₅7x²

• log₅7x

• log₅7²x

• $\log_5\left(\frac{7}{x^2}\right)$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2