document.write( "Question 905299: How do I solve the equation: $log_{2x}216=x$
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Algebra.Com's Answer #549151 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
this can be solved graphically.
\n" ); document.write( "i'm not sure if it can be solved algebraically.
\n" ); document.write( "at least i don't know how to do it.
\n" ); document.write( "by graphing i get x = 3 which satisfies the equation because:
\n" ); document.write( " $\"log%282x%2C216%29=x\"$ becomes $\"log%286%2C216%29=3\"$ when $\"x+=+3\"$
\n" ); document.write( "you can confirm the solution is correct because the law of logs states:
\n" ); document.write( " $\"log%28b%2Cx%29+=+y\"$ if and only if $\"+b%5Ey+=+x\"$
\n" ); document.write( "by that law:
\n" ); document.write( " $\"log%282x%2C216%29+=+x\"$ if and only if $\"%282x%29%5Ex+=+216\"$
\n" ); document.write( "when $\"x=3\"$ , $\"%282x%29%5Ex+=+216\"$ becomes $\"%286%29%5E3+=+216\"$ which becomes $\"216=216\"$ which is true.\r
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