document.write( "Question 457002: Solve: $\"log%28base16%29%283x+-1%29\"$ = $\"log%28base4%29%283x%29\"$ + $\"log%28base4%29%280.5%29\"$ \n" ); document.write( "

Algebra.Com's Answer #314344 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28base16%29%283x+-1%29\"$ = $\"log%28base4%29%283x%29\"$ + $\"log%28base4%29%280.5%29\"$
\n" ); document.write( "..
\n" ); document.write( "log16(3x-1)=log4(3x)+log4(0.5)
\n" ); document.write( "change of base from 16 to 4 on left side of equation
\n" ); document.write( "log4(3x-1)/log4(16)
\n" ); document.write( "log4(3x-1)/4
\n" ); document.write( "..
\n" ); document.write( "log4(3x-1)/4=log4(3x)+log4(0.5)
\n" ); document.write( "log4(3x-1)/4=log4(3x*.5=log4(3x/2)
\n" ); document.write( "log4(3x-1)=4log4(3x/2)
\n" ); document.write( "log4(3x-1)-4log4(3x/2)=0
\n" ); document.write( "log4[(3x-1)/(3x/2)^4]=0
\n" ); document.write( "convert to exponential form: (base(4) raised to log of number(0)=number,[(3x-1)/(3x/2)^4]
\n" ); document.write( "4^0=[(3x-1)/(3x/2)^4]=1
\n" ); document.write( "(3x-1)=(3x/2)^4]=81x^4/16
\n" ); document.write( "16(3x-1)=81x^448x-16=81x^4
\n" ); document.write( "81x^4-48x+16=0\r
\n" ); document.write( "\n" ); document.write( "I don't know how to solve this algebriacally, but I got answers from my graphical program on my computer.
\n" ); document.write( "x=.362459
\n" ); document.write( "or x=.66667 \n" ); document.write( "

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