Find values of a and b so that y = a·b^x and the line y = x + 5 are tangent at x = 0

Let (x,ebx) be the point of contact of y=ebx and y=10x.

10x=ebx(1)

Similarly, using your method, we get

10=bebx(2)

Now you have two equations and two unknowns. (Hint, divide two equation Follow

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.