Solving Logarithmic Functions

 $\log_3\left(x\right)=4$  

Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\log_5\left(x-7\right)=2$  
Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\log_4\left(3x+2\right)=3$  
Solve for x.

• 20.67

• 26.33

• 11

• 27.67

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

 $\log_6\left(x+5\right)+\log_6\left(4\right)=2$  
Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

 $\log_5\left(x^5\right)-\log_5\left(x^3\right)=2$  

Which of the follow best describes why  $x=-5$  is an extraneous solution to the equation above?

Hint: Try plugging in -5 and simplifying!

• -5 does not match the base of the logarithms.

• -5 is less than the output of the equation.

• Plugging in -5 for x results in a negative argument.

• Plugging in -5 for x results in a positive argument.

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.IF.B.5

 $\log_2\left(x^2+2x\right)-\log_2\left(x\right)=3$  
Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $-6\log_3\left(x-3\right)=-24$  
Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\ln\left(x^3+3x\right)-\ln\left(x\right)=4$  
Solve for x.

•  $x=99.98$  and  $x=-99.98$  (extraneous)

•  $x=99.98$  and  $x=-99.98$  , no extraneous solutions

•  $x=7.18$  and  $x=-7.18$  (extraneous)

•  $x=7.18$ and  $x=-7.18$  , no extraneous solutions

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $2\log_3\left(x+4\right)=2$  
Solve for x. Enter only numbers in your answer.

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\log_8\left(2\right)+\log_8\left(4x^2\right)=1$  
Solve for x.

•  $x=1$  and  $x=-1$  , no extraneous solutions

•  $x=1$  and  $x=-1$  (extraneous)

•  $x=4$  and  $x=-4$  , no extraneous solutions

•  $x=4$ and  $x=-4$  (extraneous)

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4