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? asked in Science & MathematicsMathematics · 8 years ago

Solve the following logarithmic equation.?

ln (x+5) - lh (x) = 1

Round off answer to 4 decimal places. Or choose "no solution."

x=???

2 Answers

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  • L. E. Gant
    Lv 7
    8 years ago
    Favorite Answer

    ln(x + 5) - ln(x) = 1

    ==> ln((x+5)/x) = 1

    ==> (x+5)/x = e

    ==> x+ 5 = e*x

    ==> x(e - 1) = 5

    ==> x = 5/(e-1)

    e = 2.71828 (approx.)

    so the rest is arithmetic.

  • KyRonn C
    8 years ago

    ln (x+5) - ln x = 1

    One rule says that:

    ln ((x+5)/x) = 1

    This means that

    e = (x+5)/x

    ex = x+5

    ex - x = 5

    x (e - 1) = 5

    x = 5/(e-1)

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