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This printable supports Common Core Mathematics Standard HSF-BF.B.5, HSF-LE.A.4

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Solving Exponential Equations, #2 (Grades 11-12)

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Solving Exponential Equations, #2

Instructions: Assume that [math]log[/math] is base 10 and [math]ln[/math] is base [math]e[/math].

1. 
What is the exact solution to [math]8*2^x = 3 ?[/math]
  1. [math]x = log_2(3/8)[/math]
  2. [math]x = log_2(3)/8[/math]
  3. [math]x = log_2(3/16)[/math]
  4. [math]x = log(3/8)[/math]
2. 
Solve exactly. [math]3*e^(2x) = 9[/math]
  1. [math]x = log(3/2)[/math]
  2. [math]x = 1/3 ln(9/2)[/math]
  3. [math]x = ln(3/2)[/math]
  4. [math]x = 1/2 ln(3)[/math]
3. 
What is the exact solution to [math]10^(4x) = e^2 ?[/math]
  1. [math]x = 1/2 ln(e)[/math]
  2. [math]x = 1/2 log(e)[/math]
  3. [math]x = 2log(e/2)[/math]
  4. [math]x = log(e/2)[/math]
4. 
Find the exact solution to the following equation. [math]2*2^x = 5[/math]
  1. [math]x = log(5/2)[/math]
  2. [math]x = 1/2 log(5)[/math]
  3. [math]x = log(5/2)/log(2)[/math]
  4. [math]x = log_2(5)[/math]
5. 
What is the exact solution to the equation [math]7e^(3x) = 1 ?[/math]
  1. [math]x = 0[/math]
  2. [math]x = 1/3 ln(1/7)[/math]
  3. [math]x = ln(1/21)[/math]
  4. [math]x = log(1/21)[/math]
6. 
Solve exactly. [math]1/2 *10^{12x} = 8[/math]
  1. [math]x = ln(4/3)[/math]
  2. [math]x = log(4/3)[/math]
  3. [math]x = 1/3 log(2)[/math]
  4. [math]x = log(1/3)[/math]
7. 
Find the exact solution to the following equation. [math]-3 * 2^{-5x} = -1/3[/math]
  1. [math]x = -2/5 log_2(1/3)[/math]
  2. [math]x = log_2(1/45)[/math]
  3. [math]x = log_2(-1/45)[/math]
  4. No solution.
8. 
Solve exactly. [math]e^(1/2 x) = 7[/math]
  1. [math]x = log(7/2)[/math]
  2. [math]x = ln(7/2)[/math]
  3. [math]x = 2 ln(7)[/math]
  4. [math]x = 1/2 ln(7)[/math]
9. 
Find the exact solution to [math]18 * 2^x = 10[/math].
  1. [math]x = ln(5/9) / ln(2)[/math]
  2. [math]x = ln(5/9)[/math]
  3. [math]x = 1/2 log(5/9)[/math]
  4. [math]x = 1/18 ln(10)[/math].
10. 
What is the exact solution to [math]2^x = 10^e ?[/math]
  1. [math]x = log_2(10^e)[/math]
  2. [math]x = ln(10^e)[/math]
  3. [math]x = log(10^e)[/math]
  4. [math]x = 1/2 log(10^e)[/math]

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