Math question – 2ln(1/2) + 2ln(1) = 2ln(2) how is that possible

-2ln(1/2) + 2ln(1) = 2ln(2)

why is this? I don’t understand how those add up to that. I know the rules like you can multiply the terms that you are adding but I don’t see how this comes out.

Properties of Logarithms
1. ln 1 = 0
2. ln ab = ln a + ln b
3. ln a
b = ln a ln b
4. ln a
r = r ln a

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4 Responses to Math question – 2ln(1/2) + 2ln(1) = 2ln(2) how is that possible

  1. Peter Blood says:

    ln x – ln y = ln (x/y)

    You have
    -2ln(1/2) + 2ln(1) = 2ln(2)

    Which is
    2ln(1) -2ln(1/2) = 2ln(2)

    1 / 0.5 = 2
    Works.

  2. ln(1) = 0 (e^0 = 1)

    ln(1/2) = -ln(2)

    The general principle is:

    ln(x^y) = y ln(x)

    Therefore, ln(1/2) = ln(2^(-1)) = – ln(2)

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