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# How calculate x from

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How calculate x from

2=-20 log10(1/1+x^2)

Guest Apr 5, 2017
#1
+1

Solve for x:
2 = -(20 log(x^2 + 1))/(log(10))

2 = -(20 log(x^2 + 1))/(log(10)) is equivalent to -(20 log(x^2 + 1))/(log(10)) = 2:
-(20 log(x^2 + 1))/(log(10)) = 2

Divide both sides by -20/(log(10)):
log(x^2 + 1) = -(log(10))/10

-(log(10))/10 = log(1/10^(1/10)):
log(x^2 + 1) = log(1/10^(1/10))

Cancel logarithms by taking exp of both sides:
x^2 + 1 = 1/10^(1/10)

Subtract 1 from both sides:
x^2 = 1/10^(1/10) - 1

Take the square root of both sides:
Answer: | x = sqrt(1/10^(1/10) - 1)        or           x = -sqrt(1/10^(1/10) - 1)

Guest Apr 5, 2017
#2
+89953
+1

2 = -20 log10(1/1+x^2)    divide both sides by -20

-1/10   = log10(1/1+x^2)

This says that

10^(-1/10)  =  1 / [ 1 + x^2 ]       exponentiate both sides to -10

10  =   [ 1 / ( 1 + x^2)]^(-10)      and we can write

10  = [ (1 + x^2) ] ^(10)     take each side to the 1/10 power

10^(1/10)  = 1 + x^2       subtract 1 from both sides

10^(1/10) - 1   = x^2      take both roots

x =  ± sqrt [10^(1/10) - 1]  ≈  ± 0.50885

CPhill  Apr 5, 2017