Solving Exponential Equations and Inequalities (Evaluation)

Solve: 7^-x = 49

• x = 1
• x = -1
• x = 2
• x = -2

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.B.5

Sovle for x:
5^{-3x - 1} = 25

• x = -1
• x = -4
• x = -3
• x = 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve for p:
4^p+2 = 64

• p = -16/9
• p = 1
• p = 8
• p = 7/6

Tags

CCSS.7.EE.B.4A

3^{2x – 6}  = 81

• x = log 4
• x = 5
• x = 4
• x = -1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve the following exponential equation:

 $3^3=3^{4x+2}$  

•  $x=\frac{1}{4}$  

•  $x=-\frac{1}{4}$  

•  $x=\frac{1}{2}$  

•  $x=-\frac{1}{2}$  

How would you solve an exponential equation like the one below:
 $4^{2x-3}=4^{6x+5}$  

• Rewrite  $4$  as  $2^2$  

• Multiply the exponents

• Set the exponents equal to each other

• Add the exponents

How would you solve an exponential equation like the one below:
 $3^{x+7}=27^{-3x-1}$  

• Rewrite  $27$  as  $3^3$  

• Multiply the exponents

• Set the exponents equal to each other

• Add the exponents

Solve the following exponential equation:
 $\left(\frac{1}{2}\right)^{2x}=4^3$  

•  $x=3$  

•  $x=-\frac{5}{2}$  

•  $x=-3$  

•  $x=\frac{5}{2}$  

Solve the following exponential inequality:

 $\frac{1}{49}<343^{2x+3}$  

•  $x>\frac{11}{6}$  

•  $x<-\frac{11}{6}$  

•  $x>-\frac{2}{3}$  

•  $x>-\frac{11}{6}$  

Solve the following exponential inequality:

 $\left(\frac{1}{64}\right)^{2x+3}\le8^x$  

•  $x\ge\frac{18}{25}$  

•  $x\ge-\frac{18}{25}$  

•  $x\ge-\frac{18}{15}$  

•  $x\le-\frac{18}{15}$