Maths
posted by Peter .
solve 3^x=4^(x2)

take ln of both sides
ln (3^x) = ln (4^(x2))
x(ln3) = (x2)(ln4)
= x(ln4)  2ln4
xln3  xln4 = 2ln4
x(ln3  ln4) = 2ln4
x = 2ln4/(ln3ln4)
or
x = 2ln4/(ln4  ln3)
if get appr. 9.638
check:
3^9.638 = appr. 39672.63
4^7.638 = 39676.6
 close enough using only 3 decimals, if I use my calculator's memory and store the full value of x, my error is 5.9x10^6