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Math - natural log

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Solve for x. (25e^0.1x)/(e^(0.1x) + 3) = 10

e^2.5x / (e^(0.1x) + 3) = 10
e^(2.5x - 0.1x) + 1/3 = 10
e^2.4x = 29/3
ln^(e^(2.4x)) = ln(29/3)
2.4x = ln(29/3)
x = 0.945

Is that correct?

  • Math - natural log -

    Let e^.1 x = y
    25 y /(y+3) = 10
    25 y = 10 y + 30
    15 y = 30
    y = 2
    so
    e^.1 x = 2
    ln e^.1x = ln 2
    .1 x = ln 2
    x = 10 ln 2
    = 6.931

  • Math - natural log -

    Express the given quantity as a single logarithm.
    ln(1+x^8)+ln(x)- ln(sin(x))

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