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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
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]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]24*e^(2x)=48[/math].
  1. [math]ln(2)/2[/math]
  2. [math]-ln(6)/(ln(5))[/math]
  3. [math]log(2)/(2log(9))[/math]
  4. [math]ln(9)/5[/math]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]7*2^(14x)=56[/math].
  1. [math]-log(2)/log(8)[/math]
  2. [math]-24[/math]
  3. [math]3/14[/math]
  4. [math]log(8)/7[/math]
Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4
Solve for x. [math]e^(4x+2)=1[/math]
  1. [math]1[/math]
  2. [math]e[/math]
  3. [math]-1/2[/math]
  4. [math]2[/math]
  5. none of these are correct
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]11*2^(7x)=121[/math].
  1. [math]-log(8)/6[/math]
  2. [math]2/log(11/2)[/math]
  3. [math]-log(8)/11[/math]
  4. [math]log(11)/(7log(2))[/math]
Grade 11 Exponents CCSS: HSF-LE.A.4
Solve for [math]x[/math] in [math]15*e^(10x)=90[/math].
  1. [math]ln(6)/10[/math]
  2. [math]log(5)/13[/math]
  3. [math]ln(15)/6[/math]
  4. [math]-8/15[/math]
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