Question #06fb2

1 Answer
Dec 13, 2016

#x = sqrt(2/pi)(10^(-4.4)) and x = -sqrt(2/pi)(10^(-4.4))#

Explanation:

Given: #85 = 173 + 10log_10(2/4pix^2)#

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

Subtract 173 from both sides:

#-88 = 10log_10(pi/2x^2)#

Divide both sides by 10:

#-8.8 = log_10(pi/2x^2)#

Make both sides the exponent of 10:

#10^(-8.8) = 10^(log_10(pi/2x^2))#

The right side simplifies because 10 is the base:

#10^(-8.8) = pi/2x^2#

Multiply both sides by #2/pi#

#x^2 = (2/pi)10^(-8.8)#

Raise both sides to the #1/2# power:

#x = +-sqrt(2/pi)(10^(-4.4))#