Conditions to drop the base

jbyx78 wrote:Hello everybody,
I have a question about exponents and bases. If 2^first expression with (or without) the variable x = 2^another expression, can I always drop the base (2) and write "first expression = another expression" ? Can I do that if 2 isn't the base but any other real number (except -1, 0, or 1) is ?

thanks a lot !

If you're asking about the scenario when 2^x = 2^y, sure, we can always say that x = y. But as you noted, we have to be careful about those scenarios when the base is -1, 0, or 1. If 1^x = 1^y, x and y can be anything. And you need to make sure that all the bases are broken down into their constituent parts. If 5 * 2^x = 10 * 2^10, to take a simple example, we obviously cannot say that x = 10, as the 10 will contribute another 2.