Solving exponential and Logarithmic Equations

Reorder

Put the steps in the correct order to solve the equation.

$$64^x=8^{\left(3x+1\right)}$$

• $$\left(8^2\right)^x=8^{\left(3x+1\right)}$$

• $$2x=3x+1$$

• $$-x=1$$

• $$x=-1$$

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2

3

4

• 1
• 2
• 3
• 4

Reorder

Put the steps in the correct order to solve the equation.

$$32^{\left(x+6\right)}\cdot\frac{1}{2}=8^{\left(x-1\right)}$$

• $$\left(2^5\right)^{\left(x+6\right)}\cdot2^{\left(-1\right)}=\left(2^3\right)^{\left(x-1\right)}$$

• $$5x+30+-1=3x-3$$

• $$5x+29=3x-3$$

• $$2x=-32$$

• $$x=-16$$

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2

3

4

5

• 1
• 2
• 3
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• 5

Multiple Choice

Solve 3³ = 3^{4x + 2}

• x = ¼
• x = -¼
• x = ½
• x = -½

Multiple Choice

Solve 8 = 2^5x+7

• x = ⅘
• x = ¼
• x = -⅘
• x = -¼

Multiple Choice

Solve for x.
$$\log_{196}\left(x\right)=\frac{1}{2}$$  

• 14

• 98

• 392

• No solution

Multiple Choice

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

• 12

• 60

• 64

• No solution

Multiple Choice

Solve for x.
$$\log_{20}\left(2x-100\right)=3$$  

• 80

• 1023

• 4050

• No solution

Multiple Choice

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

• -3

• 14

• -8

• No solution

Multiple Choice

Solve for x.
$$8+\log_6\left(x-1\right)=6$$  

• $$\frac{37}{36}$$  

• $$-\frac{1331}{8}$$  

• $$-\frac{1}{28}$$  

• 11

Multiple Choice

Solve for x.
$$-6\log_{12}\left(x-5\right)=-6$$  

• -1

• -864

• 2

• 17

Multiple Choice

Solve for x.
$$-7\log_2\left(x+9\right)=0$$  

• 6

• -1

• 1.01

• -8

Multiple Choice

Solve for x.
$$\log_3\left(7\right)+\log_3\left(2x\right)=2$$  

• $$-\frac{9}{8}$$  

• $$\frac{13}{2}$$  

• $$\frac{9}{14}$$  

• $$\frac{9}{40}$$  

Multiple Choice

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

• -2

• 0

• 1

• No solution

Multiple Choice

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

• 2, 13

• 2, -4

• 4

• 2

Multiple Select

Determine the extraneous solution(s) for the equation:  $$\log_4\left(x-6\right)+\log_4\left(x-12\right)=2$$  
Select all that apply.

• 14

• 4

• 16

• 2

Multiple Choice

Determine the correct set-up for:

log₄(x-1) - log₄(x+7) = log₄6

• log₄(x-1)/(x+7)=log₄(6)

• log₄(x-1)(x+7)=log₄(6)

• log₄(x+7)/(x-1)=log₄(6)

• (x-1)(x+7)=6

Multiple Choice

Solve:

log (x - 1) - log (x - 2) = log 5

• 7

• 4/9

• 9/4

• 1/7