Question

Solve the following expressions using logarithm and Antilogarithm .

1.

`√(0.0002851)`
2.

`\sqrt[7]{0.0005812}`
3.

`2.714^(3)`
4.

`{35.12}^{ (1)/(5) }`
5.

`{(0.07214})^{ (1)/(3) }`
​

Answer 1

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

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

• 
  `\sqrt[7]{0.0005812}` =
• 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.