Where does the graph of #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)#

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

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

#ln (x)-ln(7-x)-9=0#
#ln(x/(7-x))=9#

#(x/(7-x))=e^9#

#x=e^9*(7-x)#

#x=7*e^9-e^9*x#

#(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...