document.write( "Question 826553: Log4(x-1)+log4(3x-1)=2 \n" ); document.write( "
Algebra.Com's Answer #498171 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"log%284%2C%28x-1%29%29%2Blog%284%2C%283x-1%29%29=2\"\r
\n" ); document.write( "\n" ); document.write( "\"log%284%2C%28%28x-1%29%283x-1%29%29%29=2\"..............convert into log base \"10\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28%28x-1%29%283x-1%29%29%2Flog%284%29=2\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28%28x-1%29%283x-1%29%29=2log%284%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-1%29%283x-1%29=16\"..............solve for \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"3x%5E2-x-3x%2B1=16\"\r
\n" ); document.write( "\n" ); document.write( "\"3x%5E2-4x%2B1-16=0\"\r
\n" ); document.write( "\n" ); document.write( "\"3x%5E2-4x-15=0\"............factor completely, first replace \"-4x\" with \"-9x%2B5x\"\r
\n" ); document.write( "\n" ); document.write( "\"3x%5E2-9x%2B5x-15=0\"..............group\r
\n" ); document.write( "\n" ); document.write( "\"%283x%5E2-9x%29%2B%285x-15%29=0\"....factor out \"3x\" from the first term and \"5\" from the second term\r
\n" ); document.write( "\n" ); document.write( "\"3x%28x-3%29%2B5%28x-3%29=0\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x-3%29%283x%2B5%29+=+0\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "if\"+x-3=0\" => \"x=3\"\r
\n" ); document.write( "\n" ); document.write( "if \"3x%2B5=0\" => \"x=-5%2F3\"\r
\n" ); document.write( "\n" ); document.write( "since we have log, consider only \"x=3\" as a solution\r
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