Solving Exponential and Logarithmic Equations

For questions 1 - 3, convert each to logarithmic form.

1.    7² = 49

 log ₂ 7 = 49
 log ₄₉ 7 = 2
 log ₇ 49 = 2

2.     3³ = 27

  log ₂₇ 3 = 3
  log ₃ 3 = 27
  log ₃ 27 = 3

3.    4^0.5 = 2

  log ₄ 2 = 0.5 (or 1/2)
  log ₂ 4 = 0.5 (or 1/2)
  log _0.5 4 = 2

For questions 4 and 5, convert the logaritm to exponential form.

4.  log ₂ 512 = 9

2^5.12 = 9
2⁹ = 512
9² = 512

5. log ₃ 729= 6

 3^7.29 = 6
3⁶ = 729
 6³ = 729

6. For log _b 243 = 5, find the value of b.

  b = 4
  b = 5
  b = 3

7. For log₈ x = 1, find x.

  0
  1
  8