Question

Question #06fb2

Answer 1

`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))`