document.write( "Question 67161: what is (are) the solution(s) of the equation log sub 4 4x+2 log sub4(x+3)=2 \n" ); document.write( "
Algebra.Com's Answer #47760 by Edwin McCravy(20060)![]() ![]() You can put this solution on YOUR website! log4(4x) + 2·log4(x + 3) = 2\r\n" ); document.write( "\r\n" ); document.write( "Get the left side to a single logarithm.\r\n" ); document.write( "\r\n" ); document.write( "Use the rule\r\n" ); document.write( "\r\n" ); document.write( " n·logBA = logBAn \r\n" ); document.write( "\r\n" ); document.write( "to rewrite the second term:\r\n" ); document.write( "\r\n" ); document.write( "log4(4x) + log4(x + 3)2 = 2\r\n" ); document.write( "\r\n" ); document.write( "Use the rule:\r\n" ); document.write( "\r\n" ); document.write( " logBA + logBC = logB(AC) to rewrite the\r\n" ); document.write( "whole left side:\r\n" ); document.write( "\r\n" ); document.write( " log4[4x(x + 3)2] = 2\r\n" ); document.write( "\r\n" ); document.write( "Use the rule:\r\n" ); document.write( "\r\n" ); document.write( "logBA = C can be rewritten as A = BC \r\n" ); document.write( "\r\n" ); document.write( "to rewrite the equation:\r\n" ); document.write( "\r\n" ); document.write( " 4x(x + 3)2 = 42\r\n" ); document.write( "\r\n" ); document.write( " 4x(x + 3)(x + 3) = 16\r\n" ); document.write( "\r\n" ); document.write( "4x(x2 + 3x + 3x + 9) = 16\r\n" ); document.write( "\r\n" ); document.write( " 4x(x2 + 6x + 9) = 16\r\n" ); document.write( "\r\n" ); document.write( "To make things easier, divide both sides by 4\r\n" ); document.write( "\r\n" ); document.write( " x(x2 + 6x + 9) = 4 \r\n" ); document.write( "\r\n" ); document.write( " x3 + 6x2 + 9x = 4\r\n" ); document.write( "\r\n" ); document.write( " x3 + 4x2 + 9x - 4 = 0 \r\n" ); document.write( "\r\n" ); document.write( "There is no easy way to solve that by hand, so we\r\n" ); document.write( "use a TI-82 or higher calculator and get\r\n" ); document.write( "\r\n" ); document.write( " x = 0.3553013976 \r\n" ); document.write( "Edwin\n" ); document.write( " |