Question

Is it possible for an exponential equation to have no solutions? If so, give an example. If not, explain why.

Answer 1

A function f(x) has solutions if we can find a value to plug in that leads to 0. In other words, there are solutions to f(x) = 0. Another term for "solution" is "root" or "x intercept"

An exponential function may cross the x axis at one point only. Though there are plenty of cases when there are no solutions at all. For instance, in the case of f(x) = (2^x) + 10

The right hand side will never be equal to zero no matter what you plug in for x. The graph will never cross the axis.

To answer your question, yes it is possible to have an exponential equation to have no solutions.