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  1. 1Solving 4x−7=2x+9
  2. 2Linear cost equation
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  4. 6Weight limit word problem
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  6. 8Rate of change, cost per hour
  7. 9Finding slope then extending line
  8. 10Percent increase then decrease
  9. 11Percent: part is 18% of what
  10. 12Ratio split of 66 members
  11. 13Converting mph to ft/s
  12. 14Printer rate word problem
  13. 16Fraction from a table
  14. 17Mean shift, finding new value
  15. 19Factoring a quadratic
  16. 20Sum of roots, quadratic
  17. 21Vertex form of a parabola
  18. 24Percent growth rate, 1.03^t
  19. 26Exponential growth, doubling
  20. 27Evaluating f(−2)
  21. 28Finding a, then g(-2)
  22. 30Shifting a graph f(x−3)+1
  23. 31Circle by completing the square
  24. 34Complementary angles in a triangle
  25. 35Tangent in a right triangle
  26. 36Isosceles right triangle area
  27. 38Volume of a cylinder
  28. 39Volume of a sphere
  29. 40Scaling a box's volume
  30. 41Supplementary angles equation
  31. 42Setting up a cost equation
  32. 43Slope between two points
  33. 44x-intercept of a line
  34. 45Slope of perpendicular line
  35. 46Solving a linear system
  36. 48Solving a fraction equation
  37. 49Solving 7-3x>2x-18
  38. 50Height when planted, w=0
  39. 53Intersecting lines, find k
  40. 54System of two equations
  41. 57Product of roots
  42. 58Matching exponent bases
  43. 60Equation with same denominator
  44. 61Vertex of a parabola
  45. 63Exponential decay, halving
  46. 65Solving f(a)=21 for a quadratic
  47. 68Exponential growth, V=2500(1.04)^t
  48. 69Composing g(x)=f(x+2)-3
  49. 71Price per ounce comparison
  50. 72Percent increase
  51. 76Map scale ratio problem
  52. 77Converting rate units
  53. 78Line of best fit
  54. 79Median of a data set
  55. 80Scaling up a sample
  56. 83Ratio of flour to sugar
  57. 84Two successive percent decreases
  58. 87Triangle angle sum
  59. 88Ladder as right triangle
  60. 89Area of a trapezoid
  61. 9030-60-90 triangle sides
  62. 91Area of a circle sector
  63. 94Volume of a cone
  64. 95Cube volume to surface area
  65. 99Same-side interior angles

58Matching exponent bases

If 23x=4x+2\displaystyle 2^{3x} = 4^{x + 2}, what is the value of x\displaystyle x?

The trick is to make the bases match: since 4 = 2², rewrite 4^(x+2) as 2^(2x+4), so the exponents give 3x = 2x + 4, meaning x = 4. Check: 2^12 = 4096 and 4^6 = 4096 ✓.

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