document.write( "Question 735204: Please show how to solve:\r
\n" ); document.write( "\n" ); document.write( "Log base10(n^2 � 90n) = 3\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #854092 by MathTherapy(10801) $\"\"$ $\"About$

You can put this solution on YOUR website!

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

\n" ); document.write( "

\n" );