document.write( "Question 1106333: log↓2(6x-1)-3=2log↓2(x)\r
\n" ); document.write( "\n" ); document.write( "I don't even know where to start. \n" ); document.write( "

Algebra.Com's Answer #721345 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Note you can write \"log base 2 of x\" as \"log(2,x)\", or, better yet, \"log(2,(x))\".

\n" ); document.write( " $\"log%282%2C%286x-1%29%29-3+=+2log%282%2C%28x%29%29\"$
\n" ); document.write( " $\"log%282%2C%286x-1%29%29-log%282%2C%288%29%29+=+2log%282%2C%28x%29%29\"$ [write the constant 3 as log base 2 of something]
\n" ); document.write( " $\"log%282%2C%28%286x-1%29%2F8%29%29+=+log%282%2C%28x%5E2%29%29\"$ [rules of logarithms: difference of logs = log of quotient; log(x^n) = n*log(x)]
\n" ); document.write( " $\"%286x-1%29%2F8+=+x%5E2\"$ [if the logs of the expressions are equal, then the expressions are equal]
\n" ); document.write( " $\"6x-1+=+8x%5E2\"$
\n" ); document.write( " $\"8x%5E2-6x%2B1+=+0\"$
\n" ); document.write( " $\"%284x-1%29%282x-1%29+=+0\"$
\n" ); document.write( " $\"x+=+1%2F4\"$ or $\"+x+=+1%2F2\"$

\n" ); document.write( "Both solutions satisfy the original equation, so both are solutions. \n" ); document.write( "

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