Given that equation a ^ x-x = 0 has two real roots, the number of real roots of equation a ^ x-loga x = 0 is Same as above, I don't think so

Given that equation a ^ x-x = 0 has two real roots, the number of real roots of equation a ^ x-loga x = 0 is Same as above, I don't think so

a^x-x=0
a^x=x
There are two real roots
So y = a ^ X and y = x have two intersections A and B
a^x-loga x=0
a^x=loga x
Because a ^ X and Loga X are inverse functions, they are symmetric with respect to y = X
Then the symmetric points of a and B with respect to y = x are on loga X
And a and B are on y = X
So the point of symmetry of a and B with respect to y = x is a and B itself
So a and B are also in loga X
If there is no other intersection between a ^ X and y = x, then the symmetric points of other points on a ^ x about y = x are not on y = X
That is not on y = loga X
So the number of real roots of a ^ x-loga x = 0 is 2