How do I solve this equation?2^(x)+3^(x)=13I know that the answer is x=2 but what are the ways of solving this type of problem? Please show all your work, thanks.

Let f(x) = 2^x + 3^x Since 2^x and 3^x are strictly increasing functions, f(x) is a strictly increasing function. That is to say, if x < y, then f(x) < f(y). Strictly increasing functions are one to one. If f(x) = f(y), then x = y, So, f(x) = 13 can have at most one solution.f(0) = 2 f(1) = 5 f(2) = 13 So, we see that x = 2 is a solution.  Hence x = 2 is the only real valued solution.Best of Luck to you!If you have any questions, feel free to comment below.Happy New Year! :)