document.write( "Question 459917: How do you solve something like this:
\n" ); document.write( "2x=64\r
\n" ); document.write( "\n" ); document.write( "(2 to the x power equals 64)
\n" ); document.write( "using logarithms
\n" ); document.write( "other examples are
\n" ); document.write( "2 to the x power equals 100
\n" ); document.write( "10 to the x power equals 12
\n" ); document.write( "3 to the x power equals 48 \n" ); document.write( "

Algebra.Com's Answer #315409 by nerdybill(7384) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2%5Ex=64\"$
\n" ); document.write( "take log base 2 of both sides
\n" ); document.write( " $\"log%282%2C2%5Ex%29+=+log%282%2C64%29\"$
\n" ); document.write( " $\"log%282%2C2%5Ex%29+=+log%282%2C2%5E6%29\"$
\n" ); document.write( " $\"x+=+6\"$
\n" ); document.write( ".
\n" ); document.write( "2 to the x power equals 100
\n" ); document.write( " $\"2%5Ex+=+100\"$
\n" ); document.write( " $\"log%282%2C2%5Ex%29+=+log%282%2C100%29\"$
\n" ); document.write( " $\"x+=+log%282%2C100%29\"$
\n" ); document.write( "apply \"change of base\":
\n" ); document.write( " $\"x+=+log%28100%29%2Flog%282%29\"$
\n" ); document.write( " $\"x+=+6.644\"$
\n" ); document.write( ".
\n" ); document.write( "10 to the x power equals 12
\n" ); document.write( " $\"10%5Ex+=+12\"$
\n" ); document.write( " $\"x+=+log%2812%29\"$
\n" ); document.write( " $\"x+=+1.079\"$
\n" ); document.write( ".
\n" ); document.write( "3 to the x power equals 48
\n" ); document.write( " $\"3%5Ex+=+48\"$
\n" ); document.write( " $\"x+=+log%283%2C48%29\"$
\n" ); document.write( " $\"x+=+log%2848%29%2Flog%283%29\"$
\n" ); document.write( " $\"x+=+3.524\"$
\n" ); document.write( " \n" ); document.write( "

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