Boy isn't this fun

Can someone please tell me if this is right or wrong?

If g(x) = bx and h(x) = logbx, would the graphs of these functions intersect if b = 1? If so, at what ordered pair?

My Answer

g(x) = x and h(x) = log(x)

g(x) = x is a straight line through the Origin with a slope of 1

h(x) crosses the x-axis at (1,0) and does not intersect g(x).

log(x) = x has no solution.

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Would this be right or wrong? If it's wrong how can I answer the question. If it is partly right how can I do this problem in a way that would get me full marks? Do i need to show anything else in teh answer?

Thanks