Solve for x:
3^(4 x - 5) = 27^(-2 x - 10)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(3) (4 x - 5) = 3 log(3) (-2 x - 10)
Divide both sides by log(3):
4 x - 5 = 3 (-2 x - 10)
Expand out terms of the right hand side:
4 x - 5 = -6 x - 30
Add 6 x + 5 to both sides:
10 x = -25
Divide both sides by 10:
x = -5/2