Where does the graph of $ln (x) - (ln (7 - x)) - 9 = y$ $ln(x)-(ln(7-x))-9=y$ cross the x-axis?

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Answer 1 · 2016-02-03T15:14:08

The graph crosses the x-axis at $(6.999136, 0)$ $(6.999136, 0)$

From the given equation:
$ln (x) - ln (7 - x) - 9 = y$ $ln (x)-ln(7-x)-9=y$

set $y = 0$ $y=0$ then solve for $x$ $x$

$ln (x) - ln (7 - x) - 9 = 0$ $ln (x)-ln(7-x)-9=0$
$ln (\frac{x}{7 - x}) = 9$ $ln(x/(7-x))=9$

$(\frac{x}{7 - x}) = e^{9}$ $(x/(7-x))=e^9$

$x = e^{9} \cdot (7 - x)$ $x=e^9*(7-x)$

$x = 7 \cdot e^{9} - e^{9} \cdot x$ $x=7*e^9-e^9*x$

$(1 + e^{9}) x = 7 \cdot e^{9}$ $(1+e^9)x=7*e^9$

$(cancel((1+e^9))x)/cancel(1+e^9)=(7*e^9)/(1+e^9)$

$x=(7*e^9)/(1+e^9)$

$x=6.999136$

The graph crosses the x-axis at $(6.999136, 0)$

Kindly check the graph ....

graph{y=ln x-ln(7-x)-9[-10,10,-20,20]}

Have a nice day !!! from the Philippines...

Where does the graph of ln(x)-(ln(7-x))-9=yln(x)−(ln(7−x))−9=yln(x)-(ln(7-x))-9=y cross the x-axis?