Question: How to find the real solution where two curves intersect when solution has _Z?

I have two functions, f(x) and g(x).

Based the plot, I can see that they intersect around x equals 0, 1, around 4.5 and 10.

So I tried to find the numerical solution by solving f(x) -  g(x) for x assuming x is real.

I'm stuck here because the aswer involves RootOf and _Z and I don't know what to do next.

This is what I've tried so far:




proc (x) options operator, arrow; 18*log10(x) end proc


"g(x):=1/(2) x^(3)-8*x^(2)+(69/(2))^()*x-27"

proc (x) options operator, arrow; (1/2)*x^3-8*x^2+(69/2)*x-27 end proc


plot([f(x), g(x)], x = -1 .. 11)



`assuming`([solve(f(x)-g(x), x)], [x::real])




exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 1.505446443)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, -3.291052648)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 2.302585093)), 1







I know there's an answer to this because I can get the expected answer from Wolfram Alpha (see here).

How can I accomplish this in Maple? 

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