You can put this solution on YOUR website! 2^x + 4^x = 30
notice that 4^x = 2^2x = (2^x)^2
now let u = 2^x, then we have
u + u^2 = 30
u^2 +u -30 = 0
(u+6) * (u-5) = 0
u = -6, u = 5
observe that the log of a negative number is undefined
u = 5 is 2^x = 5, then
x = log(base 2) of 5 = ln(5) / ln(2) = 2.32
so we have x = 2.32
check this answer
2^2.32 + 4^2.32 = 30
4.99 + 24.93 = 30
29.94 = 30
30 = 30
