Question

Pls,pls,pls,help me I will give lots of pound 100+ points

Answer 1

Answer:

1. 3log(10) -2log(5) ≈ 1.60206
2. no; rules of logs apply to any base. ln(x) ≈ 2.302585×log(x)
3. no; the given "property" is nonsense

Step-by-step explanation:

1.

The given expression expression can be simplified to ...

  3log(10) -2log(5) = log(10^3) -log(5^2) = log(1000) -log(25)

  = log(1000/25) = log(40) . . . . ≠ log(5)

  ≈ 1.60206

Or, it can be evaluated directly:

  = 3(1) -2(0.69897) = 3 -1.39794

  = 1.60206

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2.

The properties of logarithms apply to logarithms of any base. Natural logs and common logs are related by the change of base formula ...

  ln(x) = log(x)/log(e) ≈ 2.302585·log(x)

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3.

The given "property" is nonsense. There is no simplification for the product of logs of the same base. There is no expansion for the log of a sum. The formula for the log of a power does apply:

  $\log(a)\log(b)=\log(a^{\log(b)})=\log(b^{\log(a)})$

Numerical evaluation of Mr. Kim's expression would prove him wrong.

  log(3)log(4) = (0.47712)(0.60206) = 0.28726

  log(7) = 0.84510

  0.28726 ≠ 0.84510

  log(3)log(4) ≠ log(7)