When determining if you can solve an exponential equation, the correct statement is: The bases on either side of the equation have to be equal. This allows you to set the exponents equal to each other, enabling you to solve for the variable.
If the bases are different, you may not be able to solve the equation using simple algebraic methods without further manipulation (such as taking logarithms). If there are variables in the base or if the bases are equal, it can still be solved by setting the exponents equal to each other.