Transcendental Numbers...1

Discussion in 'Other Pre-University Math' started by nycmathguy, Jun 1, 2022.

  1. nycmathguy

    nycmathguy

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    What is e^(pi)?

    What is pi^(e)?

    Can the above be done without a calculator?
     
    nycmathguy, Jun 1, 2022
    #1
  2. nycmathguy

    MathLover1

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    NO, have to use calculator
     
    MathLover1, Jun 1, 2022
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Ok. Got it.

    Check this out:

    Infinity...4
     
    nycmathguy, Jun 1, 2022
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  4. nycmathguy

    HallsofIvy

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    Do you remember when calculators did not exist? I do!
    We used tables of logarithms.
    [math]\log(e^{\pi}}= \pi \log(e)= 3.1416(0.4343)= 1.3644[/math].
    The you look up 0,3644 in the body of the table to see that 0.3644 is the logarithm of 2.3142. Multiplying that by 10, for the leading "1", [math]e^{\pi}= 23.142[/math].

    Similarly, [math]\log(\pi^e}= e \log(\pi)= 2.7183(0.4971)= 1.3514[/math]
    Look up 0,3514 in the body of the table to see that 0,3514 is the logarithm of 2.2459. Multiplying that by 10, for the leading "1", [math]\pi^e= 22.459[/math].
     
    HallsofIvy, May 4, 2024
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  5. nycmathguy

    RobertSmart

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    What is e^pie?
    The value of e^pie is approximately 23.1407.

    What is pi^e?
    The value of pi^e is approximately 22.4592.|

    These calculations are typically done using a calculator or computer, as they involve irrational numbers and transcendental functions. While some approximations or logarithmic methods might provide rough estimates, precise values cannot be computed accurately without the aid of a calculator.

    It is not the easy task to complete these types of question. You need to practice it more and solve a lot of assignments to get complete command on it. You can find the samples or get assignment assistance related to it at mathsassignmenthelp website. You can also contact them at: +1 (315) 557-6473.
     
    RobertSmart, May 22, 2024
    #5
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