Solving Exponential and Logarithmic Equations

Solve the equation: 

 $6^{2x}=6^{\left(-x-1\right)}$  

•  $-\frac{1}{3}$  

•  $\frac{15}{8}$  

•  $5$  

•  $\frac{19}{10}$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

Solve the equation: 

 $5^{\left(2-3x\right)}=25$  

•  $\frac{7}{5}$  

•  $-\frac{3}{4}$  

•  $-\frac{7}{6}$  

•  $0$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

Solve the equation: 

 $625^{-3x}=125^{\left(2x+2\right)}$  

•  $0$  

•  $1$  

•  $-\frac{1}{3}$  

•  $-9$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve the equation:

  $32^{\left(-3x+1\right)}=\left(\frac{1}{4}\right)^{5x}$  

• 1

•  $\frac{1}{8}$  

• 5

•  $\frac{1}{5}$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

Solve the equation:

  $4^{2x\ }=\ 7$  

• 0

• 1.311

• .364

• .702

Tags

CCSS.HSF.LE.A.4

Solve:

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Tags

CCSS.HSF.BF.B.5

Solve:

log₂(2) + log₂(8x) = 6

• x = 3

• x = 2

• x = 6

• x = 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.5

Solve:

log₃(x - 5) = 2

• 25

• 5

• 130

• 14

Tags

CCSS.HSF.BF.B.5

Solve:

ln (3x + 2) = ln (5x - 6)

• x = 1

• x = 4

• x = 2

• x = 7

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.5

Solve:

log₂ x + log₂ (x + 5) = log₂ (3x + 8)

• x = 2

• x = -4

• x = 2 and x = -4

• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4