#### Answer

$n =4.81 \approx 4.8 $

#### Work Step by Step

Given:
25 grains per square inch at a magnification of 75x.
Required:
ASTM grain-size number
Solution:
Using Equation 4.18, we find:
$N_{M}(\frac{M}{100})^{2} = 2^{n-1}$
$N_{M}$ = 25 = number of grains at magnification M (75)
$(25)(\frac{75}{100})^{2} = 2^{n-1}$,
Solving for $n$, we find:
$n = \frac{log N_{m} + 2 log \frac{M}{100}}{log 2} + 1 = \frac{log 25 + 2 log \frac{75}{100}}{log 2} +1 =4.81 $