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    I Formal definition of multiplication for real and complex numbers

    I know that the definition of multiplication for integers is just repeated addition. For example, 5 times 3 means 5 + 5 + 5, but what about if we want to extend this definition to real or complex numbers ? Like for example, what does pi times e mean ? How are we supposed to add pi to itself e...
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    B A question about rules of multiplication

    This might sound like a stupid question but I am just wondering why is it that x times yz equals xyz and not xyxz ? Why don't we distribute multiplication in this case ?
  3. L

    Why is momentum equal to mass times velocity?

    I tried searching on the internet for hours to find an answer, but I didn't find any.
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    How do you prove that ln(a^x) = xln(a) and a^x = e^xln(a) without using exponent rules?

    How did you arrive to the conclusion that ln(1/a)^x = xln(1/a) ? This is exactly what I want to prove.
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    How do you prove that ln(a^x) = xln(a) and a^x = e^xln(a) without using exponent rules?

    use power series
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    How do you prove that ln(a^x) = xln(a) and a^x = e^xln(a) without using exponent rules?

    In the book "Calculus by Michael Spivak" it says that a^x = e^xln(a) is a definition. And I am not convinced to accept this as true without a proof.
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