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10 September, 18:19

What is the value of x in the equation ln (x + 6) - ln (2x - 1) = 1?

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  1. 10 September, 18:30
    0
    1.95

    Step-by-step explanation:

    hello:

    ln (x + 6) - ln (2x - 1) = 1 ... (*)

    this expression exist : 2x-1 > 0 and x+6 > 0 means : x> 1/2 and x > - 6

    hence for : x> 1/2 (*) equivalent to ln ((x+6) / (2x-1)) = lne ... (1=lne)

    (x+6) / (2x-1) = e

    x+6 = e (2x-1) means : x+6 = 2ex-e

    -x+2ex = e+6

    x (2e-1) = e+6

    x = (e+6) / (2e-1) = (2.73+6) / (2 (2.73) - 1) = 8.73/4.46 = 1.95
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