Solve for x over the real numbers:
9^(3 x) = 4^(7 x + 3)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
6 log(3) x = 2 log(2) (7 x + 3)
Expand out terms of the right hand side:
6 log(3) x = 14 log(2) x + 6 log(2)
Subtract 14 x log(2) from both sides:
(6 log(3) - 14 log(2)) x = 6 log(2)
Divide both sides by 6 log(3) - 14 log(2):
Answer: |x = (6 log(2)) / (6 log(3) - 14 log(2))
