Properties of Logarithms

Write log_b(xy) as two logs

• log_bx+log_by
• log_bx-log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand

• A
• B
• C
• D

Tags

CCSS.HSN.RN.A.1

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

• log (a⁵ + b²⁵)
• log (a⁵ − b²⁵)
• log (ab²⁵)
• log (a⁵/b²⁵)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand log₆(5x³/y).

• log₆5x³-log₆y
• log₆5+log₆x³-log₆y
• log₆5+3log₆x-log₆y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write $\log\left(xy\right)$ as two logs

• $\ \log x\ +\ \log\ y$

• $\log x\ -\ \log\ y$

• $\log x\ \times\log y$

• $\frac{\log x}{\log y\ }$

Expand:  $\log_4\left(3x^2\right)$  

•  $2\log_43x$  

•  $2\log_43\ +\ 2\log_4x$  

•  $\log_43\ +\ 2\log_4x$  
  

•  $2\log_43\ +\ \log_4x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand:  $\log\ ab$  

•  $\log a\ -\ \log b$  

•  $b\log a$  

•  $a\log b$  

•  $\log a+\log b$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8