Solve for x:
3^(2 x - 1) = 9 2^(-x + 3)
Take the natural logarithm of both sides and use the identities log(a b) = log(a) + log(b) and log(a^b) = b log(a):
log(3) (2 x - 1) = log(2) (-x + 3) + 2 log(3)
Expand out terms of the left hand side:
2 log(3) x - log(3) = log(2) (-x + 3) + 2 log(3)
Expand out terms of the right hand side:
2 log(3) x - log(3) = -log(2) x + 3 log(2) + 2 log(3)
Add x log(2) + log(3) to both sides:
(log(2) + 2 log(3)) x = 3 log(2) + 3 log(3)
Divide both sides by log(2) + 2 log(3):
x = (3 log(2) + 3 log(3))/(log(2) + 2 log(3))==~1.85972
