![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
2/log(base x)4 + 3/log(base 4)x = 7
\n" ); document.write( "convert to Base 10
\n" ); document.write( "2/(log4/logx)+3/(logx/log4)=7
\n" ); document.write( "2logx/log4+3log4/logx=7
\n" ); document.write( "LCD:(logx)(log4)
\n" ); document.write( "2(logx)^2+3(log4)^2=7log4logx
\n" ); document.write( "log4≈.60206
\n" ); document.write( "2(logx)^2+1.08743=4.21442logx
\n" ); document.write( "2(logx)^2-4.21442logx+1.08743=0
\n" ); document.write( "solve for logx using quadratic formula:
\n" ); document.write( "logx=.30102
\n" ); document.write( "x=10^.30102
\n" ); document.write( "x≈2
\n" ); document.write( "or
\n" ); document.write( "logx=1.80618
\n" ); document.write( "x=10^1.80618
\n" ); document.write( "x≈64
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "for x=2
\n" ); document.write( "2/log(base x)4+3/log(base 4)x
\n" ); document.write( "=2/log2(4) + 3/log4(2)
\n" ); document.write( "=2/2+3/(1/2)
\n" ); document.write( "=1+6=7\r
\n" ); document.write( "\n" ); document.write( "..
\n" ); document.write( "for x=64
\n" ); document.write( "2/log(base x)4+3/log(base 4)x
\n" ); document.write( "=2/log64(4) + 3/log4(64)
\n" ); document.write( "=2/(1/3)+3/3
\n" ); document.write( "=6+1=7
\n" ); document.write( "ans:
\n" ); document.write( "x=2 or 64\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "