how to calculate A^{ } from this formula in steps?

10log_{10} (1/A^{2})= -30

Guest Feb 18, 2017

#1**0 **

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)**

Guest Feb 18, 2017

#2**0 **

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)

ElectricPavlov
Feb 19, 2017