Properties of Logarithms

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

• add

• subtract

• multiply

• divide

Tags

CCSS.HSF.BF.B.5

When you have a log expression with a number in front of it, we really need to ___________ .

• make the number an exponent at the end of the log expression.

• multiply it with the log expression.

• add it to the log expression.

• subtract it from the log expression.

Tags

CCSS.HSF.BF.B.5

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

• add

• subtract

• multiply

• divide

Tags

CCSS.HSF.BF.B.5

Simplify:  $\log_73+\log_76$  

•  $\log_79$  

•  $\log_7\left(\frac{1}{2}\right)$  

•  $\log_718$  

•  $\log_7729$  

Tags

CCSS.HSF.BF.B.5

Simplify:  $\log_4\left(x+4\right)-\log_4\left(x-5\right)$  

•  $\log_49$  

•  $\log_4\left(2x-1\right)$  

•  $\log_4\left(x^2-x-20\right)$  

•  $\log_4\left(\frac{x+4}{x-5}\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Simplify:  $2\log_3\left(11x\right)$  

•  $\log_3\left(22x\right)$  

•  $\log_3\left(121x\right)$  

•  $\log_3\left(121x^2\right)$  

•  $\log_3\left(11x^2\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Simplify:  $\frac{1}{4}\log_516+3\log_5x$  

•  $\log_5\left(4x^3\right)$  

•  $\log_5\left(2x^3\right)$  

•  $\log_5\left(6x\right)$  

•  $\log_5\left(\frac{2}{x^3}\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Simplify:  $2\log_2x-\log_2\left(x+3\right)$  

•  $\log_2\left(x^3+3x^2\right)$  

•  $\log_2\left(2x^2+6x\right)$  

•  $\log_2\left(\frac{x^2}{x+3}\right)$  

•  $\log_2\left(\frac{2x}{x+3}\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Simplify:  $\frac{1}{4}\log_281+\frac{1}{2}\log_249$  

•  $\log_221$  

•  $\log_210$  

•  $\log_2\left(\frac{3}{7}\right)$  

•  $\log_244.75$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify:  $\frac{1}{2}\log_964+\log_9x$  

•  $\log_9\left(32x\right)$  

•  $\log_9\left(\frac{32}{x}\right)$  

•  $\log_9\left(\frac{8}{x}\right)$  

•  $\log_9\left(8x\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8