Please show how to solve:
Log base10(n^2 � 90n) = 3
Thank you
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To this author, what the other person who responded wrote, as a solution to this equation, doesn't make any sense.
That's, "....n^2 - 90n = log base 10 (3) = .48
use quadratic formula and we get (note that b is --90 or 90)
n=(90+square root (90^2-4*1*-.48)) / 2 = 90"
<== Base 10 is OPTIONAL, because we work in the decimal system, so usually, base 10 is NOT entered.
Since the log argument 
MUST be greater than 0, we have: 
===> 
.
The SOLUTIONS to the INEQUALITY, 0 and 90 are the CRITICAL POINTS, with 3 intervals: Interval 1: n-values < 0
Interval 2: 0 < n-values < 90
Interval 3: n-values > 90
When tested, we find that the n-values that'll satisfy the INEQUALITY are < 0, and > 90. So, based on that, we get:
, with n < 0, or > 90.
---- Converting to EXPONENTIAL form
(n - 100)(n + 10) = 0
n - 100 = 0 OR n + 10 = 0 ----- Setting each factor equal to 0
n = 100 OR n = - 10
As seen, 100 is > 90, and - 10 is < 0, so both solutions are VALID/ACCEPTABLE!
