document.write( "Question 574529: log2x(216)=x\r
\n" ); document.write( "\n" ); document.write( "I know the answer is 3 (Calculator), but I don't know the steps required. \n" ); document.write( "

Algebra.Com's Answer #369179 by KMST(5397) $\"\"$ $\"About$

You can put this solution on YOUR website!
That answer makes sense because
\n" ); document.write( " $\"log%282x%2C216%29=x\"$ --> $\"log%282x%2C6%5E3%29=x\"$ --> $\"log%282x%2C%282%2A3%29%5E3%29=x\"$
\n" ); document.write( "Maybe you were expected to graph and check. Maybe you would transform the equation like this:
\n" ); document.write( " $\"log%282x%2C6%5E3%29=x\"$ --> $\"3log%282x%2C6%29=x\"$ --> $\"3log%283%2C6%29%2Flog%283%2C2x%29=x\"$
\n" ); document.write( "At this point, you would realize that the graphs of the functions
\n" ); document.write( " $\"y=3log%283%2C6%29%2Flog%283%2C2x%29\"$ and $\"y=x\"$ look like this, intersecting at just ore point that appears to be (3,3)
\n" ); document.write( " $\"graph%28300%2C300%2C-1%2C5%2C-6%2C12%2C3log%283%2C6%29%2Flog%283%2C2x%29%2Cx%29\"$
\n" ); document.write( "and making a further transformation, you would realize, and easily prove that x=3 is indeed the answer
\n" ); document.write( " $\"3log%283%2C%282%2A3%29%29%2Flog%283%2C%282%2Ax%29%29=x\"$ --> $\"3%28log%283%2C2%29%2B1%29=x%28log%283%2C2%29%2Blog%283%2Cx%29%29\"$ \n" ); document.write( "

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