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Common Core Standard HSF-LE.A.4 Questions

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

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Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.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]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]4*2^(7x)=16[/math].
  1. [math]8log(4)[/math]
  2. [math]1/16[/math]
  3. [math]2ln(6)[/math]
  4. [math]2/7[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]6*10^(3x)=36[/math].
  1. [math]1/3log(6)[/math]
  2. [math]log(13)[/math]
  3. [math]ln(3)[/math]
  4. [math]12[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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.
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]12*e^(4x)=42[/math].
  1. [math]log(15/2)[/math]
  2. [math]ln(13)[/math]
  3. [math]1/4ln(13/3)[/math]
  4. [math]1/2log(16)[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]18*2^(x)=90[/math].
  1. [math]log(5/2)[/math]
  2. [math]log(5)/log(2)[/math]
  3. [math]ln(10)[/math]
  4. [math]5/log(2)[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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].
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]5*2^(6x)=205[/math].
  1. [math]log(41)/(6log(2))[/math]
  2. [math]log(6)/log(2)[/math]
  3. [math]ln(2)/{7ln(41))[/math]
  4. [math]41/ln(2)[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
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]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]8*10^(16x)=2[/math].
  1. [math]log(5)/(8log(7))[/math]
  2. [math]-log(4)/(3log(6))[/math]
  3. [math]-log(2)/(8log(10))[/math]
  4. [math]log(9)/(4log(3))[/math]
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