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how to calculate A  from this formula in steps?

 

10log10 (1/A2)= -30

Guest Feb 18, 2017
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 #1
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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
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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

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