2 logs equal

Hi,

I dont know how to get this question
g(x)=loge(x)

The mining engineer, Victoria, decides that a better site for the mine is the region bounded by the graph
of g and that of a new function k: (–8, a) ¿ R, k(x) = –loge(a – x), where a is a positive real number.
i. Find, in terms of a, the x-coordinates of the points of intersection of the graphs of g and k.


so
loge(x)= - loge(a-x)

but

The answer is x= a+-( (sqrt(a^2-4)/2)
jagguyAsked:
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ozoCommented:
loge(x)= - loge(a-x)
-loge(1/x) = -loge(a-x)
1/x = a-x
1 = x(a-x)
1 = xa + x^2
x^2 + ax - 1 = 0
0

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jagguyAuthor Commented:
solving for x the answer is

x= a +- sqrt(a^2 - 4)/2

so a=1 b=a c=-1 but we have got c=1 so there is an error.
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jagguyAuthor Commented:
ok I see it

x^2-xa+1
0
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