Logarithms?

Whatever you understand underneath an 'exponential equation', the answer is most likely yes as there are many equations that have no solutions, no real solutions.

e.g.

exp(x) + 1 = 0

has no real solutions as exp(x) > 0.

Sure. e^x = 0 has no solutions.

y = e^x is positive for all values of x.

y = - 17 is negative for all values of x.

These two equations do not intersect, so there is no solution.