Solve for x over the real numbers:
(4 x-5)^(2 x+5) = 1
Take the natural logarithm of both sides:
log(4 x-5) (2 x+5) = 0
Split log(4 x-5) (2 x+5) into separate parts with additional assumptions.
Assume 4 x-5!=0 from log(4 x-5):
2 x+5 = 0 for 4 x-5!=0
or log(4 x-5) = 0
Subtract 5 from both sides:
2 x = -5 for 4 x-5!=0
or log(4 x-5) = 0
Divide both sides by 2:
x = -5/2 or log(4 x-5) = 0
Cancel logarithms by taking exp of both sides:
x = -5/2 or 4 x-5 = 1
Add 5 to both sides:
x = -5/2 or 4 x = 6
Divide both sides by 4:
Answer: |x = -5/2 or x = 3/2