Logarithms Questions

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Which question do you want to solve?

  1. Evaluate: `log_5 2 + log_5 50 - log_5 4`
  2. Evaluate: `log_49 7 + log_8 64`
  3. Solve: `log_2 8 - log_(1/2) 8`
  4. Solve for `x` if: `log_x 729 = 3`
  5. Find the value of `log root(3)(1/27)`
  6. Find `x` if: `1/2log 36 - 3log 2 = log x`
  7. If `log 2 = 0.30103` and `log 3 = 0.47712`, evaluate `log 48`
  8. Solve for `x`, given that: `log_2 5x - log_4 5x = 3`
  9. Without using logaithmic tables or calculator, evaluate:
    `(log (1/4) + log 64)/(log 32 - log (1/8))`
  10. Without using logarithms table, solve the equation:
    `log (5x - 4) = log (x - 2) + 1/3 * log 27`
  11. If `log 3 = 0.4771` and `log 5 = 0.6990`. Without using mathematical tables, evaluate:
    1. `log 150`
    2. `10 + log 45`
    3. `log sqrt(40.5)`
  12. Given: `log_8 5 = R`. Express `log_4 10` in terms of R.
  13. `log_a x, log_b x` and `log_c x` are in Arithmetic Progression (A.P), where `x ne 1`, then show that: `c^2 = (ac)^(log_a b)`
  14. Find `x` if `3 - xlog 2 = log 250`
  15. If `log x = log_5 2x`, solve for `x`
  16. Solve for `x` if: `log x = x/(50)`
  17. Solve for `r` if `log r^2 = r/(25)`
  18. Solve for `m`: `log m^2 = (log m)^2`
  19. Given: `log_9 a = log_(12) b = log_(16) (a + b)`, find the value of `a/b`
  20. Solve for `p` and `q`:
    `{((log_3 p)^2 = log_3 p^2), (log_3 (p + q) = log_3 p + log_3 q):}`
  21. Find `x` if:
    `{(4^((x/y + y/x)) = 32), (log_3 (x - y) + log_3 (x + y) = 1):}`
  22. Solve for `x`: `log 5x = 0.0075x^2`
  23. Use logarithm tables to evaluate:
    `(0.07284^2)/(root(3)(0.06195))`
  24. Evaluate using mathematical tables:
    `root(5)((41.9 times log 1.159)/(2.3 times 10^3))`
  25. Find the value of `x`, given that: `log_2 (x^2 - 2) - log_2 (1/2 x + 5) - 1 = 0`
  26. Without using mathematical tables or a calculator, evaluate: `5/6 log 64 + log 50 - 4log 2`
  27. Prove that: `log_a X + log_a Y = log_a (X*Y)`
  28. Prove that: `log_a X - log_a Y = log_a (X/Y)`
  29. Solve for `x` in the equation: `1/2 log_2 81 + log_2 (x^2 - x/3) = 1`
  30. Without using tables or calculator, simplify: `1/2 log 1600 - 2log (x/5) + log x^2`
  31. Solve the equation: `log (5x - 4) = log (x + 1) + log 4`
  32. Use logarithms to solve: `3^(x + 1) = 18.72` (give your answer correct to `3` significant figures).
  33. Given that: `log 2 = 0.301` and `log 5 = 0.699`, use these values to find `log 6.25`
  34. Given that `a = log_5 35` and `b = log_9 35`, show that:
    `log_5 21 = 1/(2b) (2ab - 2b + a)`
  35. Solve the equations: `log_b a + 2log_a b = 3` and `log_9 a + log_9 b = 3`, given that `a ne b`.
  36. If `log p = 1.813` and `log q = bar 2 .513`, find the value of `pq^2`
  37. Use logarithms to evaluate:
    `((log 7.52)^2 times (17.5)^5)/(83.92)`
  38. Find the value of `log 900`, given that `log 3 = 0.4771`
  39. Given that: `a, b, c, d` are positive integers and `log_a b = 3/2, log_c d = 5/4`. If `a - c = 9`, then find the value of `b - d`
  40. If `a^(1/(log_7 a)) = X`. What is the value of `X`?
  41. If `2log_a 36 - 2log_a 4 = 1`. Find the value of `a`.
  42. Prove that: `b^(log_b x) = x`
  43. Estimate the value of: `y = (8.64)^(2.13)`
  44. Simplify: `(log_x y)*(log_y x)`
  45. Solve: `log_2 (x - 3) + log_2 (x + 1) = 5`
  46. Given that: `log_2 3 = x, log_2 5 = y, log_2 7 = z`. Express `log_2 (15/7)` in terms of `x, y` and `z`.
  47. State the values of `r` for which the following identity is true.
    `log_5 (r + 1) + log_5 (r - 4) = log_5 (r^2 - 3r - 4)`
  48. Prove that: `log_a x = -log_(1/a) x`
  49. Find `x`: `(ln x)/x = (ln 2)/2`
  50. Simplify: `(3log_(24) 24^(-2/3))*4^(log_4 85)`
  51. Simplify: `4^(2log_4 3) + 3^(2log_3 4)`
  52. Solve graphically: `ln (3x - 2) + ln (x - 1) = 2ln x`
  53. Find the value of `x`: `log_x 9 + log_(x^2) 3 = 2.5`
  54. Given that: `log x = bar 4 .7321`, determine the value of `log root(5)(x)`
  55. Solve the equation: `log (x^2 + 5x + 7) = 0`
  56. Solve for `x` in: `(log_3 x)^2 - 1/2 log_3 x = 3/2`
  57. If `log 2 = 0.3010` and `log 3 = 0.4771`, then evaluate `log (1/(50))`
  58. What is the value of: `1/(log_5 40) + 1/(log_8 40) = ?`

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Which question do you want to solve?

  1. Evaluate: `log_5 2 + log_5 50 - log_5 4`
  2. Evaluate: `log_49 7 + log_8 64`
  3. Solve: `log_2 8 - log_(1/2) 8`
  4. Solve for `x` if: `log_x 729 = 3`
  5. Find the value of `log root(3)(1/27)`
  6. Find `x` if: `1/2log 36 - 3log 2 = log x`
  7. If `log 2 = 0.30103` and `log 3 = 0.47712`, evaluate `log 48`
  8. Solve for `x`, given that: `log_2 5x - log_4 5x = 3`
  9. Without using logaithmic tables or calculator, evaluate:
    `(log (1/4) + log 64)/(log 32 - log (1/8))`
  10. Without using logarithms table, solve the equation:
    `log (5x - 4) = log (x - 2) + 1/3 * log 27`
  11. If `log 3 = 0.4771` and `log 5 = 0.6990`. Without using mathematical tables, evaluate:
    1. `log 150`
    2. `10 + log 45`
    3. `log sqrt(40.5)`
  12. Given: `log_8 5 = R`. Express `log_4 10` in terms of R.
  13. `log_a x, log_b x` and `log_c x` are in Arithmetic Progression (A.P), where `x ne 1`, then show that: `c^2 = (ac)^(log_a b)`
  14. Find `x` if `3 - xlog 2 = log 250`
  15. If `log x = log_5 2x`, solve for `x`
  16. Solve for `x` if: `log x = x/(50)`
  17. Solve for `r` if `log r^2 = r/(25)`
  18. Solve for `m`: `log m^2 = (log m)^2`
  19. Given: `log_9 a = log_(12) b = log_(16) (a + b)`, find the value of `a/b`
  20. Solve for `p` and `q`:
    `{((log_3 p)^2 = log_3 p^2), (log_3 (p + q) = log_3 p + log_3 q):}`
  21. Find `x` if:
    `{(4^((x/y + y/x)) = 32), (log_3 (x - y) + log_3 (x + y) = 1):}`
  22. Solve for `x`: `log 5x = 0.0075x^2`
  23. Use logarithm tables to evaluate:
    `(0.07284^2)/(root(3)(0.06195))`
  24. Evaluate using mathematical tables:
    `root(5)((41.9 times log 1.159)/(2.3 times 10^3))`
  25. Find the value of `x`, given that: `log_2 (x^2 - 2) - log_2 (1/2 x + 5) - 1 = 0`
  26. Without using mathematical tables or a calculator, evaluate: `5/6 log 64 + log 50 - 4log 2`
  27. Prove that: `log_a X + log_a Y = log_a (X*Y)`
  28. Prove that: `log_a X - log_a Y = log_a (X/Y)`
  29. Solve for `x` in the equation: `1/2 log_2 81 + log_2 (x^2 - x/3) = 1`
  30. Without using tables or calculator, simplify: `1/2 log 1600 - 2log (x/5) + log x^2`
  31. Solve the equation: `log (5x - 4) = log (x + 1) + log 4`
  32. Use logarithms to solve: `3^(x + 1) = 18.72` (give your answer correct to `3` significant figures).
  33. Given that: `log 2 = 0.301` and `log 5 = 0.699`, use these values to find `log 6.25`
  34. Given that `a = log_5 35` and `b = log_9 35`, show that:
    `log_5 21 = 1/(2b) (2ab - 2b + a)`
  35. Solve the equations: `log_b a + 2log_a b = 3` and `log_9 a + log_9 b = 3`, given that `a ne b`.
  36. If `log p = 1.813` and `log q = bar 2 .513`, find the value of `pq^2`
  37. Use logarithms to evaluate:
    `((log 7.52)^2 times (17.5)^5)/(83.92)`
  38. Find the value of `log 900`, given that `log 3 = 0.4771`
  39. Given that: `a, b, c, d` are positive integers and `log_a b = 3/2, log_c d = 5/4`. If `a - c = 9`, then find the value of `b - d`
  40. If `a^(1/(log_7 a)) = X`. What is the value of `X`?
  41. If `2log_a 36 - 2log_a 4 = 1`. Find the value of `a`.
  42. Prove that: `b^(log_b x) = x`
  43. Estimate the value of: `y = (8.64)^(2.13)`
  44. Simplify: `(log_x y)*(log_y x)`
  45. Solve: `log_2 (x - 3) + log_2 (x + 1) = 5`
  46. Given that: `log_2 3 = x, log_2 5 = y, log_2 7 = z`. Express `log_2 (15/7)` in terms of `x, y` and `z`.
  47. State the values of `r` for which the following identity is true.
    `log_5 (r + 1) + log_5 (r - 4) = log_5 (r^2 - 3r - 4)`
  48. Prove that: `log_a x = -log_(1/a) x`
  49. Find `x`: `(ln x)/x = (ln 2)/2`
  50. Simplify: `(3log_(24) 24^(-2/3))*4^(log_4 85)`
  51. Simplify: `4^(2log_4 3) + 3^(2log_3 4)`
  52. Solve graphically: `ln (3x - 2) + ln (x - 1) = 2ln x`
  53. Find the value of `x`: `log_x 9 + log_(x^2) 3 = 2.5`
  54. Given that: `log x = bar 4 .7321`, determine the value of `log root(5)(x)`
  55. Solve the equation: `log (x^2 + 5x + 7) = 0`
  56. Solve for `x` in: `(log_3 x)^2 - 1/2 log_3 x = 3/2`
  57. If `log 2 = 0.3010` and `log 3 = 0.4771`, then evaluate `log (1/(50))`
  58. What is the value of: `1/(log_5 40) + 1/(log_8 40) = ?`

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