The table below shows values from the function f(x)=b^x. Identify b.

Question

Answer 1

One can easily guess that b = 8 because, for example, 64=b^2 and by taking square root of both sides we get 8= √64=√b^2 = b. On the other hand, b=8 is the only possible solution, because if another number a which a≠8 satisfies the equation f(x)=a^2 with the same values in the table, if a>8 then a^2 > 8^2 =64 which is not possible, similarly a<8 means that a^2 < 8^2 = 64 which is not possible because of the values in the table.