ZJSG09112007
contestada

Solve the following expressions using logarithm and Antilogarithm .
1.
[tex] \sqrt{0.0002851} [/tex]
2.
[tex] \sqrt[7]{0.0005812} [/tex]
3.
[tex]2.714^{3} [/tex]
4.
[tex] {35.12}^{ \frac{1}{5} } [/tex]
5.
[tex] {(0.07214})^{ \frac{1}{3} } [/tex]
​

Respuesta :

mhanifa

Answer:

  1. 0.01688496
  2. 0.3449537
  3. 0.05002308
  4. 2.0375623
  5. 0.4162862

Step-by-step explanation:

Some formulas to help

  • log ab = log a + log b
  • log a/b = log a - log b
  • log a^b = b log a
  • antilog (log a) = a, antilog is the inverse of log
  • get values of log and antilog by using calculator or online calculator ( I used online calculator for this problem)
  • round numbers as required, I left them as is

1. Let the number be x, solving to show the method

  • √0.0002851 = x
  • log √0.0002851 = log x
  • 1/2 log 0.0002851 = log x
  • 1/2(-3.545) = log x
  • log x = -1.7725
  • antilog (log x) = antilog (-1.7725)
  • x = 0.01688496

2. Short of the above method, will apply to this and following

  • [tex]\sqrt[7]{0.0005812}[/tex] =
  • antilog (1/7 log (0.0005812)) =
  • antilog (1/7(-3.23567439437)) =
  • antilog (-0.46223919919) =
  • 0.3449537

3. .........................................

  • 2.714^3 =
  • antilog (log 2.714^3) =
  • antilog (3 log 2.714) =
  • antilog (3*0.43360984332) =
  • antilog (1.30082952996) =
  • 0.05002308

4..........................................

  • 35.12^(1/5) =
  • antilog (1/5 log (35.12)) =
  • antilog (1/5*1.54555450723)
  • antilog (0.30911090144) =
  • 2.0375623

5. .........................................

  • (0.07214)^(1/3) =
  • antilog ( 1/3 log (0.07214)) =
  • antilog (1/3*(-1.14182386202 )) =
  • antilog ( --0.380607954 )=
  • 0.4162862

Let me know if anything is not clear. Hope it helps.

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