Solving exponential equations with x as the exponent

[Tyrion101]

My confusion comes from basic exponent rules and whether or not both sides of an equation have to have the same level of exponent, when you reduce the base for solving. If one side can have an exponent of 3, does the other side also have to be reduced to something that would also have an exponent of 3? 9^2 does equal 81, but is that wrong if the other side can be reduced to a 3rd power, and can't be for a 2nd? I hope I'm making sense.

 

[Mark44]

My confusion comes from basic exponent rules and whether or not both sides of an equation have to have the same level of exponent, when you reduce the base for solving. If one side can have an exponent of 3, does the other side also have to be reduced to something that would also have an exponent of 3? 9^2 does equal 81, but is that wrong if the other side can be reduced to a 3rd power, and can't be for a 2nd? I hope I'm making sense.

The exponents don't have to be the same, but the bases have to be the same if you're using this idea: a^m = aⁿ $\Rightarrow$ m = n.

 

[Tyrion101]

Ok I think I understand

 

[1MileCrash]

Just to nit pick, that is true when a =\= 1 and a =\= 0.