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Lubov Fominskaja [6]
3 years ago
14

Solve the following expressions using logarithm and Antilogarithm .

Mathematics
1 answer:
katrin [286]3 years ago
5 0

Answer:

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

Step-by-step explanation:

<u>Some formulas to help</u>

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

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.

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Answer with Step-by-step explanation:

We are given that

Total dogs=24

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a.We have to find the probability that the pet is male, given that it is cat.

It means we have to find P(Male/cat)  

Conditional probability: P(A/B)=\frac{P(A\cap B)}{P(B)}

P(Cat)=\frac{18}{42}

P(male cat)=\frac{6}{42}

P(Male/cat)=\frac{\frac{6}{42}}{\frac{18}{42}}

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P(female)=\frac{28}{42}

P(Cat/Female)=\frac{\frac{12}{42}}{\frac{28}{42}}=\frac{12}{28}=0.43

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P(female/dog)=\frac{\frac{16}{42}}{\frac{24}{42}}

P(female/dog)=\frac{16}{24}=0.67

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Answer:

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2. Distribute

-5 - 10k - 8 ( -4 + 5k )

-5 - 10k + 32 - 40k

3. Add the numbers

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4. Add the same term to both sides of the equation

27 - 10k - 40k

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Answer:

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