Why do you think you are dealing with an exponential function?Hello everyone,
I believe this is a very silly question.
I've solved this one, but one thing bothers me. Solution includes 2, and I see 0 is smaller than 1 - but the definition for exponential function is for every a^x, a>0, in this case if x=2, a=0
I'm not sure what you mean by this. That's not a definition; I suppose you mean you have been told that a^x is called an exponential function only when a>0. But that doesn't mean that a^x is not defined unless a>0. Surely you learned long ago that 0^x = 0 for x non-zero, and that x^0 = 1 for x non-zero. Those facts don't change when you learn about exponential functions. And (as lev888 hinted) no one says you have to call this an exponential function.View attachment 24175
Hello everyone,
I believe this is a very silly question.
I've solved this one, but one thing bothers me. Solution includes 2, and I see 0 is smaller than 1 - but the definition for exponential function is for every a^x, a>0, in this case if x=2, a=0
It will help if you show your work in finding the solution; then I can make more specific comments on steps, and where you could determine whether 2 is part of the solution set.I thought that it was an exponential function because the inequation is not always true for x<2 (like exponential function, not defined for a<0, so i made a conclusion based on that) . Nevermind, I'm still in highschool so I do not undestand math absolutely clear only by only solving problems and not learning theory.
Thanks @Dr.Peterson , I I got it (as always when you explain).
Well, in my workbook there is the correct solution for every given problem. When I solved the problem, my solution was 2<x<3 and the solution in the book was 2<=x<3. Part that I did not understand is 2<=x.
Maybe I should have reviwed the case when x=2 for this specific problem?