If x^a+x^b = x^c then what is c in terms of a and b?
1 Answer
Apr 14, 2016
There is no expression for
Its value would depend on
Explanation:
I think this question is inspired by the identities:
x^a * x^b = x^(a+b)
(x^a)^b = x^(ab)
However, when we get to:
x^a+x^b = x^c
there is no simple expression for
Taking logs of both sides we get:
log(x^a+x^b) = log(x^c) = c log(x)
So:
c = log(x^a+x^b)/log(x) = log_x(x^a+x^b)
A particular concrete example would be:
2^1 + 2^1 = 4 = 2^2
4^1 + 4^1 = 8 = 4^(3/2)