4^x+3^x=9^x
find x thanks
4^x+3^x=9^x
4^x+3^x=3^(2x)
4^x = 3^(2x) - 3^x)
4^x = 3^x(3^x - 1
(4/3)^x = 3^x - 1
preliminary check:
if x = 1
4+3 = 7 < 9
if x = 2
16 + 9 = 25 < 81
..
if x = 6
4^6 + 3^6 = 4825 < 9^6
for x ≥ 1, the gap between LS and RS is increasing, and RS > LS
let's look at the graph of y = 4^x + 3^x and y = 9^x
http://www.wolframalpha.com/input/?i=plot+y+%3D+4%5Ex+%2B+3%5Ex+,+y+%3D+9%5Ex
There appears to be a solution at appr .7
Using such methods as Newton's Method we could get a better approximation of
x = appr. .731774
check with your calculator, it works.