Answer:
If the curves are interesting at point, they must have a solution for the equation
[tex]f(x) = g(x)[/tex]
if this equation has roots, that means they intersect, otherwise they don't.
the equation is
[tex] log_2(x)= 2^x-2\\ \text{add 2 on both sides} \\ 2+log_2(x) =2^x \\ \text{two can be written as, } log_2(2^2) \\ \text{Since } log_a(a)=1 \text{ and } log_a(x^m)=m\times log_a(x) \\ \text{ Now, sicne the base is same, use the addition property of Logarithm} \\ log_a(m)+log_a(n)=log_a(m\times n) \\ log_2(4x)=2^x \\ \text{now, if you look closely, if you put x=1, you will get LHS=RHS.} [/tex]
put x=1 in any of the function, to get y coordinate
the answer is (1,0)
