Solve for A:
(10 log(1/A^2))/(log(10)) = -30
Divide both sides by 10/(log(10)):
log(1/A^2) = -3 log(10)
-3 log(10) = log(1/10^3) = log(1/1000):
log(1/A^2) = log(1/1000)
Cancel logarithms by taking exp of both sides:
1/A^2 = 1/1000
Take the reciprocal of both sides:
A^2 = 1000
Take the square root of both sides:
Answer: |A = 10 sqrt(10) or A = -10 sqrt(10)
Divide both sides by 10 to get
log(1/a^2) = -3
1/a^2 = 10^-3
1/a^2 = .001
1/.001 = a^2
1000 = a^2
a = + or - 31.622 (10 x sqrtr10)