Solve for x over the real numbers:
2^(4 x + 16) = 6^(5 - 7 x)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(2) (4 x + 16) = log(6) (5 - 7 x)
Expand out terms of the left hand side:
4 log(2) x + 16 log(2) = log(6) (5 - 7 x)
Expand out terms of the right hand side:
4 log(2) x + 16 log(2) = 5 log(6) - 7 log(6) x
Subtract 16 log(2) - 7 x log(6) from both sides:
(4 log(2) + 7 log(6)) x = 5 log(6) - 16 log(2)
Divide both sides by 4 log(2) + 7 log(6):
Answer: |x = (5 log(6) - 16 log(2))/(4 log(2) + 7 log(6)) = - 0.139181898....
