What is x? *log is log base 5*

-9 + log₅ (-4x)   = -7     add 9 to both sides

log₅ (-4x)  = 2       this says that

5²   = -4x      divide both sides by -4

5² / - 4  = x    

- 25 /  4   = x

Solve for x:
(log(-4 x))/(log(5))-9 = -7

Add 9 to both sides:
(log(-4 x))/(log(5)) = 2

Multiply both sides by log(5):
log(-4 x) = 2 log(5)

2 log(5)  =  log(5^2)  =  log(25):
log(-4 x) = log(25)

Cancel logarithms by taking exp of both sides:
-4 x = 25

Divide both sides by -4:
Answer: |  x = -25/4