Question #06fb2

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Answer 1 · 2016-12-13T17:56:04

$x = \sqrt{\frac{2}{π}} (10^{- 4.4}) and x = - \sqrt{\frac{2}{π}} (10^{- 4.4})$ $x = sqrt(2/pi)(10^(-4.4)) and x = -sqrt(2/pi)(10^(-4.4))$

Given: $85 = 173 + 10 {log}_{10} (\frac{2}{4} π x^{2})$ $85 = 173 + 10log_10(2/4pix^2)$

NOTE: I am assuming that the logarithm is base 10.

Subtract 173 from both sides:

$- 88 = 10 {log}_{10} (\frac{π}{2} x^{2})$ $-88 = 10log_10(pi/2x^2)$

Divide both sides by 10:

$- 8.8 = {log}_{10} (\frac{π}{2} x^{2})$ $-8.8 = log_10(pi/2x^2)$

Make both sides the exponent of 10:

$10^{- 8.8} = 10^{{log}_{10} (\frac{π}{2} x^{2})}$ $10^(-8.8) = 10^(log_10(pi/2x^2))$

The right side simplifies because 10 is the base:

$10^{- 8.8} = \frac{π}{2} x^{2}$ $10^(-8.8) = pi/2x^2$

Multiply both sides by $\frac{2}{π}$ $2/pi$

$x^{2} = (\frac{2}{π}) 10^{- 8.8}$ $x^2 = (2/pi)10^(-8.8)$

Raise both sides to the $\frac{1}{2}$ $1/2$ power:

$x = \pm \sqrt{\frac{2}{π}} (10^{- 4.4})$ $x = +-sqrt(2/pi)(10^(-4.4))$