Condensing/ Expanding/ Solving Logs

Condense

• logxyz³
• log(xy/z³)
• logx+logy+logz³
• logx³y³z³

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand

• A
• B
• C
• D

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

log_b(M+N)=log_bM+log_bN

• False: It's supposed to be log_bM*log_bN
• True
• False: It's supposed to be log(M+N)/logb
• False: It's supposed to be log_b(MN)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve:

 $\log_9\left(x\right)+\log_9\left(x+2\right)=\log_9\left(35\right)\$  

• x = 5

• x = -7

• x = { 5, -7 }

• x = { -7, -13 }

Solve:
 $\log_3\left(2x-6\right)=\log_3\left(3x-7\right)$  

• x = -3 

• x = 14

• x = -8

• No solution

Solve: 

 $\log\ \left(9-x\right)=\log\ \left(2x-6\right)$  

• x = 5

• x = -11

• x =  $\frac{18}{19}$  

• x = -4

Solve:

 $\log_2\left(x+4\right)-\log_2\left(7\right)\ =\ 2$  

• x =  $\frac{160}{3}$  

• x = 24

• x = 7

• x =  $-\frac{80}{3}$  

Solve:
 $\log_8\left(4x+4\right)\ =\ 2$  

• x = 15

• x = 12

• x = 10

• x = 3

Solve: 
 $\log_3\left(x-4\right)-\log_3\left(x\right)=1$  

• x = -2

• x = 0

• x = 1

• No solution

Solve: 
 $\log_8\left(x\right)+\log_8\left(x+2\right)=1$  

• x = { 2, 13 }

• x = { 2, -4 }

• x = 4

• x = 2