Question #60774

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Answer 1 · 2016-05-09T05:38:41

$x = (5+5e^4)/(e^4-1)~~5.187$

We will use the following properties of logarithms :

with these, we have

$ln(x+5)-ln(x-5) = 4$

(note that as the $ln$ function only takes positive values, we must restrict $x$ to be greater than $5$ , or else we would have $x-5 < 0$ )

$=> ln((x+5)/(x-5)) = 4$

$=> e^(ln((x+5)/(x-5))) = e^4$

$=> (x+5)/(x-5) = e^4$

$=> x + 5 = e^4x - 5e^4$

$=> e^4x - x = 5 + 5e^4$

$=> (e^4-1)x = 5+5e^4$

$:. x = (5+5e^4)/(e^4-1)~~5.187$